Stability and optimal decay for the 3D anisotropic magnetohydrodynamic equations

被引:0
作者
Yang, Wan-Rong [1 ]
Fang, Cao [1 ]
机构
[1] North Minzu Univ, Sch Math & Informat Sci, Yinchuan 750021, Peoples R China
基金
中国国家自然科学基金;
关键词
anisotropic; decay rate; magnetohydrodynamic equation; stability; GLOBAL WELL-POSEDNESS; LARGE-TIME BEHAVIOR; 3-D MHD SYSTEM; DISSIPATION; EXISTENCE;
D O I
10.1111/sapm.12731
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This paper investigates the stability problem and large time behavior of solutions to the three-dimensional magnetohydrodynamic equations with horizontal velocity dissipation and magnetic diffusion only in the x2$x_2$ direction. By applying the structure of the system, time-weighted methods, and the method of bootstrapping argument, we prove that any perturbation near the background magnetic field (1, 0, 0) is globally stable in the Sobolev space H3(R3)$H<^>3(\mathbb {R}<^>3)$. Furthermore, explicit decay rates in H2(R3)$H<^>2(\mathbb {R}<^>3)$ are obtained. Motivated by the stability of the three-dimensional Navier-Stokes equations with horizontal dissipation, this paper aims to understand the stability of perturbations near a magnetic background field and reveal the mechanism of how the magnetic field generates enhanced dissipation and helps stabilize the fluid.
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页数:46
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