TITLE:
The 2D MHD Systems with Vertical Dissipation and Vertical Dissipation Magnetic Diffusion
AUTHORS:
Xiaoting Yang
KEYWORDS:
MHD Equation, Global Regularity, Vertical Dissipation
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.9 No.2,
June
26,
2019
ABSTRACT:
In this paper, we study the global regularity of the classical solution of the 2D incompressible magnetohydrodynamic equation with vertical dissipation and vertical magnetic dissipation. We show that any solution of the second component (u2, b2) has a global L2r -bound, where r satisfies and the boundary does not grow faster thanas r increases.