• Publications
  • Influence
Global well-posedness of the three-dimensional viscous primitive equations of large scale ocean and atmosphere dynamics
In this paper we prove the global existence and uniqueness (regularity) of strong solutions to the three-dimensional viscous primitive equations, which model large scale ocean and atmosphereExpand
  • 290
  • 46
  • PDF
Global Regularity Criterion for the 3D Navier–Stokes Equations Involving One Entry of the Velocity Gradient Tensor
In this paper we provide a sufficient condition, in terms of only one of the nine entries of the gradient tensor, that is, the Jacobian matrix of the velocity vector field, for the global regularityExpand
  • 141
  • 9
  • PDF
Regularity Criteria for the Three-dimensional Navier-Stokes Equations
In this paper we consider the three-dimensional Navier-Stokes equations subject to periodic boundary condi- tions or in the whole space. We provide suYcient conditions, in terms of one component ofExpand
  • 158
  • 7
  • PDF
Global Well-Posedness and Finite-Dimensional Global Attractor for a 3-D Planetary Geostrophic Viscous Model
In this paper we consider a three-dimensional planetary geostrophic viscous model of the gyre-scale mid-latitude ocean. We show the global existence and uniqueness of the weak and strong solutions toExpand
  • 96
  • 7
  • PDF
Two regularity criteria for the 3D MHD equations
This work establishes two regularity criteria for the 3D incompressible MHD equations. The first one is in terms of the derivative of the velocity field in one direction while the second one requiresExpand
  • 201
  • 6
  • PDF
Global regularity for the 2D MHD equations with mixed partial dissipation and magnetic diffusion
Abstract Whether or not classical solutions of the 2D incompressible MHD equations without full dissipation and magnetic diffusion can develop finite-time singularities is a difficult issue. A majorExpand
  • 230
  • 4
  • PDF
The Navier-Stokes equations on the rotating 2-D sphere: Gevrey regularity and asymptotic degrees of freedom
Abstract. In this article we prove a Gevrey class global regularity to the Navier-Stokes equations on the rotating two dimensional sphere, S2 - a fundamental model that arises naturally in largeExpand
  • 85
  • 4
The 2D Incompressible Magnetohydrodynamics Equations with only Magnetic Diffusion
TLDR
This paper examines the global (in time) regularity of classical solutions to the two-dimensional (2D) incompressible magnetohydrodynamics (MHD) equations with only magnetic diffusion. Expand
  • 105
  • 4
  • PDF
Global Regularity for the Two-Dimensional Anisotropic Boussinesq Equations with Vertical Dissipation
This paper establishes the global in time existence of classical solutions to the two-dimensional anisotropic Boussinesq equations with vertical dissipation. When only vertical dissipation isExpand
  • 107
  • 3
  • PDF
Global well-posedness of the 3D primitive equations with horizontal viscosity and vertical diffusivity
In this paper, we consider the 3D primitive equations of oceanic and atmospheric dynamics with only horizontal eddy viscosities in the horizontal momentum equations and only vertical diffusivity inExpand
  • 18
  • 3
  • PDF