Chongsheng Cao

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 regularity of strong solutions to the three-dimensional Navier–Stokes equations in the whole space, as well as for the case of periodic boundary conditions.

Global regularity results for the 2D Boussinesq equations with vertical dissipation

Article history: Received 13 October 2010 Revised 12 May 2011 Available online 28 May 2011 MSC: 35A05 35B45 35B65 76D03 76D09

The 2D Incompressible Magnetohydrodynamics Equations with only Magnetic Diffusion

This paper examines the global (in time) regularity of classical solutions to the two-dimensional (2D) incompressible magnetohydrodynamics (MHD) equations with only magnetic diffusion. Here the magnetic diffusion is given by the fractional Laplacian operator

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

(-\Delta)^\beta

Regularity Criterion for Solutions of Three-Dimensional Turbulent Channel Flows

. We establish the global regularity for the case when

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

\beta>1

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

. This result significantly improves previous work which requires

Global well-posedness of the three-dimensional viscous primitive equations of large scale ocean and atmosphere dynamics

\beta>\frac{3}{2}

Global regularity for the 2D MHD equations with mixed partial dissipation and magnetic diffusion

and brings us closer to the resolution of the well-known global regularity problem on the 2D MHD equations with standard Laplacian magnetic diffusion, namely, the case when

Two regularity criteria for the 3D MHD equations

\beta=1