# positions[].label
University Distinguished Professor and Owen Professor of Mathematics

# overview
My research in applied and computational mathematics lies at the interface between rigorous applied analysis and physical applications. Most of my work has been focused on the development of analytical and computational techniques for investigating nonlinear phenomena. Specifically, in studying the Euler and the Navier-Stokes equations of incompressible and compressible fluids, and other related nonlinear partial differential equations. Such equations arise as models in a wide range of applications in nonlinear science and engineering. The applications include, but are not limited to, fluid mechanics, oceanic and atmospheric dynamics and their coupling with moisture micro-physics in clouds formation, turbulence, chemical reactions, nonlinear fiber optics, control theory and data assimilation for weather and climate prediction.

# keywords[]
4007 Control Engineering, Mechatronics And Robotics

# keywords[]
Global Regularity Of Decimated Helical Navier-stokes Equations

# keywords[]
Inviscid Regularization Of Euler Equations

# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
Cyclonic And Anticyclonic Coherent Structures

# keywords[]
Coarse Mesh Measurements Of Only One Component Of The Velocity Field

# keywords[]
Regularization Of The Navier-stokes Equations

# keywords[]
Regularization Of The Nonlinear Schrodinger Equation

# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
Regularization Of The Navier-stokes Equations

# keywords[]
Inviscid Regularization Of Euler Equations

# keywords[]
Moisture Model For Warm Clouds With Phase Transition

# keywords[]
Well-posedness For Nonlinear Moisture Dynamics

# keywords[]
4007 Control Engineering, Mechatronics And Robotics

# keywords[]
4903 Numerical And Computational Mathematics

# keywords[]
Onsager's Conjecture And Conservation Of Energy For Euler Equations

# keywords[]
Loss Of Smoothness For The Three-dimensional Euler Equations

# keywords[]
4012 Fluid Mechanics And Thermal Engineering

# educationAndTraining[].organization.label
Indiana University Bloomington - (Bloomington, Indiana, United States)

# educationAndTraining[].organization.label
Technion - Israel Institute of Technology - (Haifa, Israel)

# educationAndTraining[].organization.label
Technion - Israel Institute of Technology - (Haifa, Israel)

# awardsAndHonors[].label
SIAG Analysis of Partial Differential Equations Prize

# publications[].label
GLOBAL WELL-POSEDNESS OF A SYSTEM OF NONLINEARLY COUPLED KDV EQUATIONS OF MAJDA AND BIELLO

# publications[].label
Assimilation of nearly turbulent Rayleigh-Bnard flow through  vorticity or local circulation measurements: a computational study

# publications[].label
Persistence of invariant sets for dissipative evolution equations

# publications[].label
ON THE NUMBER OF DETERMINING NODES FOR THE 2D NAVIER-STOKES EQUATIONS

# publications[].label
Entire solutions of hydrodynamical equations with exponential  dissipation

# publications[].label
ON A CRITERION FOR LOCATING STABLE STATIONARY SOLUTIONS TO THE NAVIER-STOKES EQUATIONS

# publications[].label
Global regularity and convergence of a Birkhoff-Rott-alpha approximation  of the dynamics of vortex sheets of the 2D Euler equations

# publications[].label
Long-time behavior of a two-layer model of baroclinic quasi-geostrophic turbulence

# publications[].label
The primitive equations approximation of the anisotropic horizontally  viscous Navier-Stokes equations

# publications[].label
Preserving dissipation in approximate inertial forms for the Kuramoto-Sivashinsky equation

# publications[].label
Global well-posedness of the 3D primitive equations with horizontal  viscosity and vertical diffusivity

# publications[].label
Gevrey regularity of the global attractor of the 3D Navier-Stokes-Voight  equations

# publications[].label
Asymptotic expansions in time for rotating incompressible viscous fluids

# publications[].publisher
European Mathematical Society - EMS - Publishing House GmbH

# publications[].label
Global Existence of Weak Solutions to the Compressible Primitive  Equations of Atmospheric Dynamics with Degenerate Viscosities

# publications[].label
Entire Solutions of Hydrodynamical Equations with Exponential Dissipation

# publications[].label
Vanishing viscosity as a selection principle for the Euler equations:  The case of 3D shear flow

# publications[].label
Long-time limit for a class of quadratic infinite-dimensional dynamical systems inspired by models of viscoelastic fluids

# publications[].label
On the Higher-Order Global Regularity of the Inviscid  Voigt-Regularization of Three-Dimensional Hydrodynamic Models

# publications[].label
On the effect of fast rotation and vertical viscosity on the lifespan of the $3D$ primitive equations

# publications[].label
On the Effect of Fast Rotation and Vertical Viscosity on the Lifespan of the 3D Primitive Equations.

# publications[].label
On the Global Regularity of a Helical-Decimated Version of the 3D Navier-Stokes Equations

# publications[].label
Global Stabilization of the Navier-Stokes-Voight and the damped  nonlinear wave equations by finite number of feedback controllers

# publications[].label
Finite determining parameters feedback control for distributed nonlinear  dissipative systems - a computational study

# publications[].label
PERSISTENCY OF ANALYTICITY FOR NONLINEAR WAVE EQUATIONS: AN ENERGY-LIKE APPROACH

# publications[].label
Convergence of the 2D Euler-alpha to Euler equations in the Dirichlet case: Indifference to boundary layers

# publications[].label
ON THE DYNAMICS OF ROTATING ELASTIC BEAMS

# publications[].label
Global regularity for a Birkhoff-Rott-alpha approximation of the dynamics of vortex sheets of the 2D Euler equations

# publications[].label
The Navier-Stokes equations on the rotating 2-D sphere: Gevrey regularity and asymptotic degrees of freedom

# publications[].label
ON APPROXIMATE INERTIAL MANIFOLDS TO THE NAVIER-STOKES EQUATIONS

# publications[].label
Global well-posedness for a rapidly rotating convection model of tall columnar structure in the limit of infinite Prandtl number

# publications[].label
Downscaling the 2D Benard Convection Equations Using Continuous Data  Assimilation

# publications[].label
Abridged Continuous Data Assimilation for the 2D Navier-Stokes Equations Utilizing Measurements of Only One Component of the Velocity Field

# publications[].label
Mathematical Advances in Geophysical Fluid Dynamics

# publications[].publisher
European Mathematical Society - EMS - Publishing House GmbH

# publications[].label
Data Assimilation algorithm for 3D Bnard convection in porous media  employing only temperature measurements

# publications[].label
GLOBAL WELL-POSEDNESS OF A THREE-DIMENSIONAL BRINKMAN-FORCHHEIMER-BENARD CONVECTION MODEL IN POROUS MEDIA

# publications[].publisher
American Institute of Mathematical Sciences (AIMS)

# publications[].label
Regularity Criterion for Solutions of Three-Dimensional Turbulent  Channel Flows

# publications[].label
On Energy Conservation for the Hydrostatic Euler Equations: An Onsager  Conjecture

# publications[].label
Hadamard well-posedness for a hyperbolic equation of viscoelasticity  with supercritical sources and damping

# publications[].label
Attractor dimension and small length scale estimates for the three-dimensional Navier-Stokes equations

# publications[].label
Global Well-Posedness of the Three-Dimensional Primitive Equations with Only Horizontal Viscosity and Diffusion

# publications[].label
Determining modes and Grashof number in 2D turbulence: a numerical case study

# publications[].label
USE OF APPROXIMATE INERTIAL MANIFOLDS IN BIFURCATION CALCULATIONS

# publications[].label
Continuous data assimilation for the three-dimensional Brinkman-Forchheimer-extended Darcy model

# publications[].label
On convergence of trajectory attractors of the 3D Navier-Stokes-alpha model as alpha approaches 0

# publications[].label
Continuous Data Assimilation with Stochastically Noisy Data

# publications[].label
$C^{0,α}$ boundary regularity for the pressure in weak solutions of   the $2d$ Euler equations

# publications[].label
Analysis of a Mixture Model of Tumor Growth

# publications[].label
ON THE COMPUTATION OF INERTIAL MANIFOLDS

# publications[].label
Trivial stationary solutions to the Kuramoto-Sivashinsky and certain nonlinear elliptic equations

# publications[].label
Dissipation Length Scale Estimates for Turbulent Flows: A Wiener Algebra Approach

# publications[].label
GLOBAL STABILITY OF LARGE SOLUTIONS TO THE 3D NAVIER-STOKES EQUATIONS

# publications[].label
Analyticity of the attractor and the number of determining nodes for a weakly damped driven nonlinear Schrodinger equation

# publications[].label
A determining form for the damped driven nonlinear Schrodinger equation-Fourier modes case

# publications[].label
Order reduction of nonlinear dynamic models for distributed reacting systems

# publications[].label
Finite-time blowup and ill-posedness in Sobolev spaces of the inviscid primitive equations with rotation

# publications[].label
Analyticity of essentially bounded solutions to semilinear parabolic systems and validity of the Ginzburg-Landau equation

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
On the radius of analyticity of solutions to the cubic Szego equation

# publications[].publisher
European Mathematical Society - EMS - Publishing House GmbH

# publications[].label
Global Well--posedness of the Three-dimensional Viscous Primitive  Equations of Large Scale Ocean and Atmosphere Dynamics

# publications[].label
Trivial Stationary Solutions to the Kuramoto-Sivashinsky and Certain Nonlinear Elliptic Equations

# publications[].label
The postprocessing Galerkin and nonlinear Galerkin methods - A truncation analysis point of view

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
Postprocessing the Galerkin method: The finite-element case

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
A determining form for the damped driven Nonlinear Schrdinger  Equation- Fourier modes case

# publications[].label
ON THE HIGHER-ORDER GLOBAL REGULARITY OF THE INVISCID VOIGT-REGULARIZATION OF THREE-DIMENSIONAL HYDRODYNAMIC MODELS

# publications[].publisher
American Institute of Mathematical Sciences (AIMS)

# publications[].label
On the Domain of Analyticity and Small Scales for the Solutions of the  Damped-driven 2D Navier-Stokes Equations

# publications[].label
Regularization modeling for large-eddy simulation of homogeneous isotropic decaying turbulence

# publications[].label
A data assimilation algorithm: the paradigm of the 3D Leray-alpha model  of turbulence

# publications[].label
Global Regularity for an Inviscid Three-dimensional Slow Limiting Ocean  Dynamics Model

# publications[].label
Regularity "in Large" for the 3D Salmon's Planetary Geostrophic Model of  Ocean Dynamics

# publications[].label
Enhanced Simulation of the Indian Summer Monsoon Rainfall Using Regional Climate Modeling and Continuous Data Assimilation

# publications[].label
Estimating the number of asymptotic degrees of freedom for nonlinear dissipative systems

# publications[].label
Determining projections and functionals for weak solutions of the Navier-Stokes equations

# publications[].label
Non-uniqueness of Weak Solutions to Hyperviscous Navier-Stokes Equations  -- On Sharpness of J.-L. Lions Exponent

# publications[].label
DETERMINING FINITE VOLUME ELEMENTS FOR THE 2D NAVIER-STOKES EQUATIONS

# publications[].label
On the Global Regularity of a Helical-decimated Version of the 3D  Navier-Stokes Equations

# publications[].label
Gevrey Regularity for Nonlinear Analytic Parabolic Equations on the Sphere

# publications[].label
Global Attractors and Determining Modes for the 3D Navier-Stokes-Voight  Equations

# publications[].label
A Computational Investigation of the Finite-Time Blow-Up of the 3D  Incompressible Euler Equations Based on the Voigt Regularization

# publications[].label
A Beale-Kato-Majda breakdown criterion for an Oldroyd-B fluid in the creeping flow regime

# publications[].label
On the regularization mechanism for the periodic Korteweg-de Vries  equation

# publications[].label
One-dimensional parametric determining form for the two-dimensional  Navier-Stokes equations

# publications[].label
Euler Equations of Incompressible Ideal Fluids

# publications[].label
A Computational Study of a Data Assimilation Algorithm for the Two-dimensional Navier-Stokes Equations

# publications[].label
On the Clark-alpha model of turbulence: global regularity and long-time dynamics

# publications[].label
On the rate of convergence of the two-dimensional $alpha$-models of  turbulence to the Navier-Stokes equations

# publications[].label
Local and Global Well-posedness of Strong Solutions to the 3D Primitive  Equations with Vertical Eddy Diffusivity

# publications[].label
Global well-posedness for the 2D Boussinesq system with anisotropic viscosity and without heat diffusion

# publications[].label
Abridged continuous data assimilation for the 2D Navier-Stokes equations  utilizing measurements of only one component of the velocity field

# publications[].label
Gevrey Regularity for the Attractor of the 3D Navier-Stokes-Voight Equations

# publications[].label
Order reduction for nonlinear dynamic models of distributed reacting systems

# publications[].label
Analyticity of the attractor and the number of determining nodes for a weakly damped driven nonlinear Schrodinger equation

# publications[].label
On the backward behavior of some dissipative evolution equations

# publications[].label
ON SOME DISSIPATIVE FULLY DISCRETE NONLINEAR GALERKIN SCHEMES FOR THE KURAMOTO-SIVASHINSKY EQUATION

# publications[].label
Global well-posedness of strong solutions to a tropical climate model

# publications[].publisher
American Institute of Mathematical Sciences (AIMS)

# publications[].label
The effect of nonlocal interactions on the dynamics of the Ginzburg-Landau equation

# publications[].label
Global well-posedness of the three-dimensional viscous primitive equations of large scale ocean and atmosphere dynamics

# publications[].label
Well-Posedness of Hibler's Dynamical Sea-Ice Model

# publications[].label
A Beale-Kato-Majda breakdown criterion for an Oldroyd-B fluid in the  creeping flow regime

# publications[].label
A unified approach to determining forms for the 2D Navier - Stokes equations - the general interpolants case

# publications[].label
Existence and uniqueness of weak solutions to viscous primitive  equations for certain class of discontinuous initial data

# publications[].label
Spectral Filtering of Interpolant Observables for a Discrete-in-time  Downscaling Data Assimilation Algorithm

# publications[].label
A Note on the Regularity of Inviscid Shell Model of Turbulence

# publications[].label
A ``horizontal" hyper--diffusion $3-D$ thermocline planetary geostrophic  model: well-posedness and long time behavior

# publications[].label
Finite-Time Blowup for the Inviscid Primitive Equations of Oceanic and Atmospheric Dynamics

# publications[].label
The Navier-Stokes-alpha model of fluid turbulence

# publications[].label
On the Convergence Rate of the Euler-alpha, an Inviscid Second-Grade Complex Fluid, Model to the Euler Equations

# publications[].label
Global Well-posedness of a System of Nonlinearly Coupled KdV equations  of Majda and Biello

# publications[].label
Stochastic attractors for shell phenomenological models of turbulence

# publications[].label
On the domain of analyticity and small scales for the solutions of the damped-driven 2D Navier-Stokes equations

# publications[].label
ANALYSIS AND COMPUTATION OF A DISCRETE KDV-BURGERS TYPE EQUATION WITH FAST DISPERSION AND SLOW DIFFUSION

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
Sharp estimates for the number of degrees of freedom for the  damped-driven 2D Navier--Stokes equations

# publications[].label
Global well-posedness for the primitive equations coupled to nonlinear moisture dynamics with phase changes

# publications[].label
Global Well-Posedness of a 3D MHD Model in Porous Media

# publications[].label
Higher-Order Global Regularity of an Inviscid Voigt-Regularization of  the Three-Dimensional Inviscid Resistive Magnetohydrodynamic Equations

# publications[].label
Determining form and data assimilation algorithm for weakly damped and  driven Korteweg-de Vries equaton- Fourier modes case

# publications[].label
Analytical Study of Certain Magnetohydrodynamic-alpha Models

# publications[].label
Well-posedness of Hibler's dynamical sea-ice model

# publications[].label
Global well-posedness for models of shallow water in a basin with a varying bottom

# publications[].label
THE INVISCID LIMIT FOR THE 2D NAVIER-STOKES EQUATIONS IN BOUNDED DOMAINS

# publications[].publisher
American Institute of Mathematical Sciences (AIMS)

# publications[].label
Simulations de l'coulement turbulent marin avec un modle de  dconvolution

# publications[].label
Gevrey regularity for nonlinear analytic parabolic equations

# publications[].label
Regularity of coupled two-dimensional nonlinear Fokker-Planck and Navier-Stokes systems

# publications[].label
A Computational Study of a Data Assimilation Algorithm for the  Two-dimensional Navier--Stokes Equations

# publications[].label
Spectral scaling of the Leray-alpha model for two-dimensional turbulence

# publications[].label
The 3D Incompressible Euler Equations with a Passive Scalar: A Road to Blow-Up?

# publications[].label
Long-time limit for a class of quadratic infinite-dimensional dynamical  systems inspired by models of viscoelastic fluids

# publications[].label
Postprocessing the Galerkin method: A novel approach to approximate inertial manifolds

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
Fully discrete numerical schemes of a data assimilation algorithm: uniform-in-time error estimates

# publications[].label
Distributed and boundary control of the viscous Burgers' equation

# publications[].label
Zero Mach Number Limit of the Compressible Primitive Equations Part I: Well-prepared Initial Data

# publications[].label
Continuous data assimilation for the three-dimensional  Navier-Stokes-$alpha$

# publications[].label
Regularity criterion for solutions of three-dimensional turbulent channel flows

# publications[].label
Efficient dynamical downscaling of general circulation models using continuous data assimilation

# publications[].label
Higher-Order Global Regularity of an Inviscid Voigt-Regularization of the Three-Dimensional Inviscid Resistive Magnetohydrodynamic Equations

# publications[].label
Continuous data assimilation for the three-dimensional Navier-Stokes-alpha model

# publications[].label
On the effect of rotation on the life-span of analytic solutions to the  $3D$ inviscid primitive equations

# publications[].label
Traveling Wave Solutions for a Class of One-Dimensional Nonlinear Shallow Water Wave Models

# publications[].label
Analytic study of shell models of turbulence

# publications[].label
Feedback Control of Nonlinear Dissipative Systems by Finite Determining  Parameters - A Reaction-diffusion Paradigm

# publications[].label
On the rate of convergence of the nonlinear Galerkin methods

# publications[].label
Continuous data assimilation for the three-dimensional  Brinkman-Forchheimer-extended Darcy model

# publications[].publisher
American Institute of Mathematical Sciences (AIMS)

# publications[].label
Global regularity for a Birkhoff-Rott-alpha approximation of the  dynamics of vortex sheets of the 2D Euler equations

# publications[].label
Global well-posedness for the lake equations

# publications[].label
The inviscid limit for the $2d$ Navier-Stokes equations in bounded  domains

# publications[].label
Inertial Manifolds for Certain Sub-Grid Scale $alpha$-Models of  Turbulence

# publications[].label
On the convergence of solutions of the Leray-/alpha model to the trajectory attractor of the 3D Navier-Stokes system

# publications[].publisher
American Institute of Mathematical Sciences (AIMS)

# publications[].label
Continuous data assimilation with stochastically noisy data

# publications[].label
Young measure approach to computing slowly advancing fast oscillations

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
A determining form for the two-dimensional Navier-Stokes equations: The Fourier modes case

# publications[].label
A connection between the Camassa-Holm equations and turbulent flows in channels and pipes

# publications[].label
The vanishing viscosity as a selection principle for the Euler equations: The case of 3D shear flow

# publications[].label
Onsager's Conjecture for Subgrid Scale $alpha$-Models of Turbulence

# publications[].label
Efficient Dynamical Downscaling of General Circulation Models Using  Continuous Data Assimilation

# publications[].label
Global well-posedness of a three-dimensional  Brinkman-Forchheimer-Bnard convection model in porous media

# publications[].label
INVARIANT HELICAL SUBSPACES FOR THE NAVIER-STOKES EQUATIONS

# publications[].label
APPROXIMATE INERTIAL MANIFOLDS FOR THE KURAMOTO-SIVASHINSKY EQUATION - ANALYSIS AND COMPUTATIONS

# publications[].label
Approximation of 2D Euler Equations by the Second-Grade Fluid Equations  with Dirichlet Boundary Conditions

# publications[].label
Global Attractors and Determining Modes for the 3D Navier-Stokes-Voight Equations

# publications[].label
Global regularity for a rapidly rotating constrained convection model of  tall columnar structure with weak dissipation

# publications[].label
Nonlinear Schrodinger-Helmholtz equation as numerical regularization of the nonlinear Schrodinger equation

# publications[].label
Euler equations for incompressible ideal fluids

# publications[].label
Analytical study of certain magnetohydrodynamic-alpha models

# publications[].label
A Posteriori Regularity of the Three-dimensional Navier-Stokes Equations  from Numerical Computations

# publications[].label
Asymptotic states of a Smoluchowski equation

# publications[].label
A dynamic-kinematic 3D model for density-driven ocean circulation flows:  Construction, global well-posedness and dynamics

# publications[].label
Global well-posedness for the thermodynamically refined passively  transported nonlinear moisture dynamics with phase changes

# publications[].label
Global well-posedness and finite-dimensional global attractor for a 3-D planetary geostrophic viscous model

# publications[].label
A Determining Form for the 2D Rayleigh-Bnard Problem

# publications[].label
On the Charney Conjecture of Data Assimilation Employing Temperature  Measurements Alone: The Paradigm of 3D Planetary Geostrophic Model

# publications[].label
Stochastic Attractors for Shell Phenomenological Models of Turbulence

# publications[].label
Continuous data assimilation for the 2D Benard convection through velocity measurements alone

# publications[].label
Euler equations for incompressible ideal fluids

# publications[].label
Stability of Two-dimensional Viscous Incompressible Flows Under  Three-dimensional Perturbations and Inviscid Symmetry Breaking

# publications[].label
Simulations of turbulent ocean flow using a deconvolution model

# publications[].label
Super-exponential convergence rate of a nonlinear continuous data  assimilation algorithm: The 2D Navier-Stokes equations paradigm

# publications[].label
Global Regularity and Convergence of a Birkhoff-Rott-alpha Approximation of the Dynamics of Vortex Sheets of the Two-Dimensional Euler Equations

# publications[].label
ON THE RATE OF CONVERGENCE OF THE TWO-DIMENSIONAL alpha-MODELS OF TURBULENCE TO THE NAVIER-STOKES EQUATIONS

# publications[].label
Gevrey regularity for nonlinear analytic parabolic equations

# publications[].label
An approximate inertial manifolds approach to postprocessing the Galerkin method for the Navier-Stokes equations

# publications[].label
REGULARITY OF SOLUTIONS AND THE CONVERGENCE OF THE GALERKIN METHOD IN THE GINZBURG-LANDAU EQUATION

# publications[].label
Continuous and Discrete Data Assimilation with Noisy Observations for  the Rayleigh-Benard Convection: A Computational Study

# publications[].label
Global well-posedness of strong solutions to the 3D primitive equations with horizontal eddy diffusivity

# publications[].label
A determining form for the subcritical surface quasi-geostrophic  equation

# publications[].label
Determining nodes for extended dissipative systems

# publications[].label
Strong solutions to the 3D primitive equations with only horizontal  dissipation: near $H^1$ initial data

# publications[].label
Global Well-posedness of the 3D Primitive Equations With Partial  Vertical Turbulence Mixing Heat Diffusion

# publications[].label
Dissipativity and Gevrey regularity of a Smoluchowski equation

# publications[].label
Global Well-posedness of Strong Solutions to the 3D Primitive Equations  with Horizontal Eddy Diffusivity

# publications[].label
Long-time Behavior of a Two-layer Model of Baroclinic Quasi-geostrophic  Turbulence

# publications[].label
Planar limits of three-dimensional incompressible flows with helical  symmetry

# publications[].label
On convergence of trajectory attractors of the 3D Navier - Stokes-$alpha$ model as $alpha$ approaches 0

# publications[].label
EXPONENTIAL DECAY-RATE OF THE POWER SPECTRUM FOR SOLUTIONS OF THE NAVIER-STOKES EQUATIONS

# publications[].label
On the uniqueness of weak solutions to the Ericksen-Leslie liquid  crystal model in $mathbb R^2$

# publications[].label
An Inviscid Regularization for the Surface Quasi-Geostrophic Equation

# publications[].label
Numerical criterion for the stabilization of steady states of the Navier-Stokes equations

# publications[].label
GLOBAL EXISTENCE AND UNIQUENESS OF WEAK SOLUTIONS OF THREE-DIMENSIONAL EULER EQUATIONS WITH HELICAL SYMMETRY IN THE ABSENCE OF VORTICITY STRETCHING

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
Cluster formation in complex multi-scale systems

# publications[].label
The Camassa-Holm equations and turbulence

# publications[].label
FEEDBACK CONTROL OF NONLINEAR DISSIPATIVE SYSTEMS BY FINITE DETERMINING PARAMETERS - A REACTION-DIFFUSION PARADIGM

# publications[].publisher
American Institute of Mathematical Sciences (AIMS)

# publications[].label
Nonlinear Schrodinger-Helmholtz Equation as Numerical Regularization of  the Nonlinear Schrodinger Equation

# publications[].label
Hadamard well-posedness for a hyperbolic equation of viscoelasticity with supercritical sources and damping

# publications[].label
Onsager's conjecture for subgrid scale alpha-models of turbulence

# publications[].label
On the Clark-alpha model of turbulence: global regularity and long--time  dynamics

# publications[].label
On the convergence rate of the Euler-$alpha$, an inviscid second-grade  complex fluid, model to the Euler equations

# publications[].label
Global well-posedness for passively transported nonlinear moisture  dynamics with phase changes

# publications[].label
Algebraic Bounds on the Rayleigh-Bnard attractor

# publications[].label
Data assimilation algorithm for 3D Benard convection in porous media employing only temperature measurements

# publications[].label
Uniform in time error estimates for fully discrete numerical schemes of  a data assimilation algorithm

# publications[].label
Planar Limits of Three-Dimensional Incompressible Flows with Helical Symmetry

# publications[].label
Regularity Criteria for the Three-dimensional Navier-Stokes Equations

# publications[].label
On the Regularization Mechanism for the Periodic Korteweg-de Vries Equation

# publications[].label
Global Well-posedness for the Primitive Equations Coupled to Nonlinear  Moisture Dynamics with Phase Changes

# publications[].label
On the Radius of Analyticity of Solutions to the Cubic Szeg Equation

# publications[].label
Modulation theory for self-focusing in the nonlinear  Schrdinger-Helmholtz equation

# publications[].label
Statistical properties of nonlinear shell models of turbulence from linear advection models: rigorous results

# publications[].label
Sharp Lower Bounds for the Dimension of the Global Attractor of the  Sabra Shell Model of Turbulence

# publications[].label
Finite-time Blowup for the Inviscid Primitive Equations of Oceanic and  Atmospheric Dynamics

# publications[].label
Recent Advances Concerning Certain Class of Geophysical Flows

# publications[].label
Loss of smoothness and energy conserving rough weak solutions for the 3d  Euler equations

# publications[].label
Cluster formation in complex multi-scale systems

# publications[].label
ON THE STATISTICAL PROPERTIES OF THE 3D INCOMPRESSIBLE NAVIER-STOKES-VOIGT MODEL

# publications[].label
Downscaling data assimilation algorithm with applications to statistical  solutions of the Navier-Stokes equations

# publications[].label
Analysis of a mixture model of tumor growth

# publications[].label
A Kinematic-Dynamic 3D Model for Density-Driven Ocean Flows: Construction, Global Well-Posedness, and Dynamics

# publications[].label
Slow observables of singularly perturbed differential equations

# publications[].label
Approximation of 2D Euler Equations by the Second-Grade Fluid Equations with Dirichlet Boundary Conditions

# publications[].label
C-1 approximations of inertial manifolds for dissipative nonlinear equations

# publications[].label
Modulation Theory for Self-Focusing in the Nonlinear Schrodinger-Helmholtz Equation

# publications[].label
Local Well-posedness of Strong Solutions to the Three-dimensional  Compressible Primitive Equations

# publications[].label
Global gevrey regularity for the Benard convection in a porous medium with zero Darcy-Prandtl number

# publications[].label
Global Existence and Uniqueness of Weak Solutions of 3-D Euler Equations  with Helical Symmetry in the Absence of Vorticity Stretching

# publications[].label
Zero Mach Number Limit of the Compressible Primitive Equations:  Ill-prepared Initial Data

# publications[].label
A data assimilation algorithm for the subcritical surface  quasi-geostrophic equation

# publications[].label
Finite-time Blowup and Ill-posedness in Sobolev Spaces of the Inviscid  Primitive Equations with Rotation

# publications[].label
Attractors for the Two-Dimensional NavierStokes- Model: An -Dependence Study

# publications[].label
A Tropical Atmosphere Model with Moisture: Global Well-posedness and  Relaxation Limit

# publications[].label
Global Well-posedness of the Three-dimensional Viscous and Inviscid  Simplified Bardina Turbulence Models

# publications[].label
Trajectory attractor approximation of the 3D Navier-Stokes system by a Leray-alpha model

# publications[].label
On the incompressible limit of a strongly stratified heat conducting  fluid

# publications[].label
The damped-driven 2D Navier-Stokes system on large elongated domains

# publications[].label
A posteriori regularity of the three-dimensional Navier-Stokes equations from numerical computations

# publications[].label
Continuous Data Assimilation for a 2D Bnard Convection System through  Horizontal Velocity Measurements Alone

# publications[].label
Efficient methods using high accuracy approximate inertial manifolds

# publications[].label
Trajectory attractor approximation of the 3D Navier-Stokes system by a Leray -model

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A unified approach to determining forms for the 2D Navier-Stokes  equations - the general interpolants case

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Asymptotic behavior of viscous 1-D scalar conservation laws with neumann boundary conditions

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An inviscid regularization for the surface quasi-geostrophic equation

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The 3D incompressible Euler equations with a passive scalar: a road to  blow-up?

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Discrete data assimilation in the Lorenz and 2D Navier-Stokes equations

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EXPONENTIAL CONVERGENCE OF THE GALERKIN APPROXIMATION FOR THE GINZBURG-LANDAU EQUATION

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GALERKIN PROJECTIONS AND THE PROPER ORTHOGONAL DECOMPOSITION FOR EQUIVARIANT EQUATIONS

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Uniform in time error estimates for a finite element method applied to a  downscaling data assimilation algorithm for the Navier-Stokes equations

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Analytic Study of Shell Models of Turbulence

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Global well-posedness of strong solutions to a tropical climate model

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Convergence of the 2D Euler-$alpha$ to Euler equations in the Dirichlet  case: indifference to boundary layers

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Analysis and Computation of a Discrete KdV-Burgers Type Equation with  Fast Dispersion and Slow Diffusion

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Global Regularity Criterion for the 3D Navier-Stokes Equations Involving One Entry of the Velocity Gradient Tensor

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The Lorenz equation as a metaphor for the Navier-Stokes equations

# publications[].publisher
American Institute of Mathematical Sciences (AIMS)

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Determining modes for continuous data assimilation in 2D turbulence

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A modified-Leray-alpha subgrid scale model of turbulence

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COMPUTATIONAL-EFFICIENCY AND APPROXIMATE INERTIAL MANIFOLDS FOR A BENARD CONVECTION SYSTEM

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Local and Global Well-Posedness of Strong Solutions to the 3D Primitive Equations with Vertical Eddy Diffusivity

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Global Well-Posedness of the Primitive Equations of Large-Scale Ocean  Dynamics with the Gent-McWilliams-Redi Eddy Parametrization Model

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On the effect of rotation on the life-span of analytic solutions to the   $3D$ inviscid primitive equations

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A study of the Navier-Stokes-alpha model for two-dimensional turbulence

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Global regularity criterion for the 3D Navier-Stokes equations involving  one entry of the velocity gradient tensor

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Exponential tracking and approximation of inertial manifolds for dissipative nonlinear equations

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ON THE EVOLUTION OF NEARLY CIRCULAR VORTEX PATCHES

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Recent Advances Concerning Certain Class of Geophysical Flows

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A unified approach to determining forms for the 2D Navier-Stokes equations - the general interpolants case

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Well-posedness of strong solutions to the anelastic equations of  stratified viscous flows

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Sharp estimates for the number of degrees of freedom for the damped-driven 2-D Navier-Stokes equations

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Mathematics and Turbulence: where do we stand?

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Rigorous estimates of small scales in turbulent flows

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Continuous Data Assimilation Using General Interpolant Observables

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Parameterizing the global attractor of the navier-stokes equations by nodal values

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Global well-posedness for a rapidly rotating convection model of tall  columnar structure in the limit of infinite Prandtl number

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ONSAGER CONJECTURE ON THE ENERGY-CONSERVATION FOR SOLUTIONS OF EULER EQUATION

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On the backward behavior of some dissipative evolution equations

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Global Well-posedness of an Inviscid Three-dimensional  Pseudo-Hasegawa-Mima Model

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C0, boundary regularity for the pressure in weak solutions of the 2d Euler equations.

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Epidemic spread in populations at demographic equilibrium

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INVARIANT MEASURES FOR THE 3D NAVIER-STOKES-VOIGT EQUATIONS AND THEIR NAVIER-STOKES LIMIT

# publications[].publisher
American Institute of Mathematical Sciences (AIMS)

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On the Well-posedness of Reduced $3D$ Primitive Geostrophic Adjustment  Model with Weak Dissipation

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The primitive equations as the small aspect ratio limit of the  Navier-Stokes equations: rigorous justification of the hydrostatic  approximation

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Small viscosity sharp estimates for the global attractor of the 2-D damped-driven Navier-Stokes equations

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DETERMINING NODES, FINITE-DIFFERENCE SCHEMES AND INERTIAL MANIFOLDS

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Continuous Data Assimilation for the 2D Bnard Convection through  Velocity Measurements Alone

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Hlder regularity of the pressure for weak solutions of the 3D Euler  equations in bounded domains

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On the uniqueness of weak solutions to the Ericksen-Leslie liquid crystal model in R-2

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Viscosity versus vorticity stretching: Global well-posedness for a family of Navier-Stokes-alpha-like models

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Global Well-Posedness of the 2D Boussinesq Equations with Vertical Dissipation

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Well-posedness of Hibler's dynamical sea-ice model

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Postprocessing Fourier spectral methods: The case of smooth solutions

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Inertial manifolds and Gevrey regularity for the Moore-Greitzer model of an axial-flow compressor

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Mathematics and turbulence: where do we stand?

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A horizontal hyper-diffusion three-dimensional thermocline planetary geostrophic model: well-posedness and long-time behaviour

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Enhanced Simulation of the Indian Summer Monsoon Rainfall Using Regional  Climate Modeling and Continuous Data Assimilation

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Asymptotic Expansions in Time for Rotating Incompressible Viscous Fluids

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Sharp lower bounds for the dimension of the global attractor of the sabra shell model of turbulence

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Introduction to Special Issue: Incompressible Fluids, Turbulence and Mixing

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Global strong solutions for the three-dimensional Hasegawa-Mima model  with partial dissipation

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Onsager's conjecture in bounded domains for the conservation of entropy  and other companion laws

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Invariant measures for the 3D Navier-Stokes-Voigt equations and their  Navier-Stokes limit

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Global Well-posedness of the 3D Primitive Equations with Only Horizontal  Viscosity and Diffusion

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Inertial Manifolds for Certain Subgrid-Scale alpha-Models of Turbulence

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

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Onsager's Conjecture for the Incompressible Euler Equations in Bounded  Domains

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On the Effect of Rotation on the Life-Span of Analytic Solutions to the 3D Inviscid Primitive Equations

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Dissipative length scale estimates for turbulent flows - a Wiener  algebra approach

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Continuous Data Assimilation Using General Interpolant Observables

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Global Well-Posedness of the 3D Primitive Equations with Partial Vertical Turbulence Mixing Heat Diffusion

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Continuous data assimilation with blurred-in-time measurements of the  surface quasi-geostrophic equation

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A discrete data assimilation scheme for the solutions of the 2D  Navier-Stokes equations and their statistics

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Global well-posedness of the 2D Boussinesq equations with vertical  dissipation

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LOSS OF SMOOTHNESS AND ENERGY CONSERVING ROUGH WEAK SOLUTIONS FOR THE 3d EULER EQUATIONS

# publications[].publisher
American Institute of Mathematical Sciences (AIMS)

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Continuous and discrete data assimilation with noisy observations for the Rayleigh-Benard convection: a computational study

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Spectral scaling of the Leray-$alpha$ model for two-dimensional  turbulence

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GLOBAL EXISTENCE THEORY FOR A GENERALIZED GINZBURG-LANDAU EQUATION

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$C^{0,alpha}$ boundary regularity for the pressure in weak solutions of  the $2d$ Euler equations

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On the Statistical Properties of the 3D Incompressible  Navier-Stokes-Voigt Model

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On the Extension of Onsager's Conjecture for General Conservation Laws

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On the domain of analyticity for solutions of second order analytic nonlinear differential equations

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Non-viscous Regularization of the Davey-Stewartson Equations: Analysis  and Modulation Theory

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Global Well-Posedness of an Inviscid Three-Dimensional Pseudo-Hasegawa-Mima Model

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The primitive equations approximation of the anisotropic horizontally   viscous Navier-Stokes equations

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Discrete Data Assimilation in the Lorenz and 2D Navier--Stokes Equations

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STABILITY OF TWO-DIMENSIONAL VISCOUS INCOMPRESSIBLE FLOWS UNDER THREE-DIMENSIONAL PERTURBATIONS AND INVISCID SYMMETRY BREAKING

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

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ON THE EFFECTIVENESS OF THE APPROXIMATE INERTIAL MANIFOLD - A COMPUTATIONAL STUDY

# researcherOn[].label
Mathematical Study of Certain Geophysical Problems:  Data Assimilation Algorithms and Mathematical-Analysis of the Primitive Equations

# researcherOn[].awardedBy.label
United States Department of the Navy - (Arlington, Virginia, United States)

# streetAddress
Texas A&M University; Mathematics; 3368 TAMU

# inTheNews[].label
Seven Texas A&M Faculty Members Awarded With University Distinguished Professorships