The 2D MHD equations with horizontal dissipation and horizontal magnetic diffusion

被引：150
|
作者：
Cao, Chongsheng [1 ]
Regmi, Dipendra [2 ]
Wu, Jiahong [2 ]
机构：
[1] Florida Int Univ, Dept Math, Miami, FL 33199 USA
[2] Oklahoma State Univ, Dept Math, Stillwater, OK 74078 USA
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2013年 / 254卷 / 07期
基金：
美国国家科学基金会;
关键词：
2D MHD equations; Global regularity; Horizontal dissipation; MAGNETOHYDRODYNAMICS;
D O I：
10.1016/j.jde.2013.01.002
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper studies the global regularity of classical solutions to the 2D incompressible magnetohydrodynamic (MHD) equations with horizontal dissipation and horizontal magnetic diffusion. It is shown here that the horizontal component of any solution admits a global (in time) bound in any Lebesgue space L-2r with 1 <= r < infinity and the bound grows no faster than the order of root rlogr as r increases. In addition, we establish a conditional global regularity in terms of the (LtLx infinity)-L-2-norm of the horizontal component and the global regularity of a slightly regularized version of the aforementioned MHD equations. (C) 2013 Elsevier Inc. All rights reserved.
引用
收藏
页码：2661 / 2681
页数：21
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