Jiahong Wu

Behavior of solutions of 2D quasi-geostrophic equations

We study solutions to the 2D quasi-geostrophic (QGS) equation

Regularity of Hölder continuous solutions of the supercritical quasi-geostrophic equation

\frac{\partial \theta}{\partial t}+u\cdot\nabla\theta + \kappa (-\Delta)^{\alpha}\theta=f

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

and prove global existence and uniqueness of smooth solutions if

Bounds and New Approaches for the 3D MHD Equations

\alpha\in (\frac{1}{2},1]

Inviscid limit for vortex patches

; weak solutions also exist globally but are proven to be unique only in the class of strong solutions. Detailed aspects of large time approximation by the linear QGS equation are obtained.

The 2D Incompressible Magnetohydrodynamics Equations with only Magnetic Diffusion

This paper derives regularity criteria for the generalized magnetohydrodynamics (MHD) equations, a system of equations resulting from replacing the Laplacian −Δ in the usual MHD equations by a fractional Laplacian (−Δ)α. These criteria impose assumptions on the velocity field u alone and sharpen a result of He and Xin (2005). In addition, these criteria apply to the incompressible Navier–Stokes equations and improve some existing results.

Viscous and inviscid magneto-hydrodynamics equations

Abstract We present a regularity result for weak solutions of the 2D quasi-geostrophic equation with supercritical ( α 1 / 2 ) dissipation ( − Δ ) α : If a Leray–Hopf weak solution is Holder continuous θ ∈ C δ ( R 2 ) with δ > 1 − 2 α on the time interval [ t 0 , t ] , then it is actually a classical solution on ( t 0 , t ] .

THE QUASI-GEOSTROPHIC EQUATION AND ITS TWO REGULARIZATIONS

The two-dimensional (2D) quasi-geostrophic (QG) equation is a 2D model of the 3D incompressible Euler equations, and its dissipative version includes an extra term bearing the operator