Affiliation:
1. Department of Mathematics Hangzhou Dianzi University Hangzhou China
2. School of Mathematics Shanghai University of Finance and Economics Shanghai China
Abstract
In this article, we consider the Cauchy problem of the three‐dimensional incompressible magnetohydrodynamic (MHD) system with only horizontal dissipation and vertical magnetic diffusion near the equilibrium. We establish the global a priori estimate of the smooth solution for this system, with initial data
sufficiently small in
, by using the special structure of the nonlinear terms and the anisotropic Sobolev inequality.
Funder
Science Fund for Distinguished Young Scholars of Zhejiang Province
National Natural Science Foundation of China
National Key Defense Laboratory of Computational Physics