Stability of stationary solution for the compressible viscous magnetohydrodynamic equations with large potential force in bounded domain

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:262

Article

Li, Yeping¹  Yang, Xiongfeng^2,3 

[1] East China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China

[2] Shanghai Jiao Tong Univ, MOE LSC, Sch Math Sci, Shanghai 200240, Peoples R China

[3] Shanghai Jiao Tong Univ, SHL MAC, Shanghai 200240, Peoples R China

关键词: Magnetohydrodynamic equations;    Initial-boundary problem;    Potential force;    Stationary solution;    Stability criterion;   

DOI  :  10.1016/j.jde.2016.11.021

来源: Elsevier

【 摘 要 】

In this paper, we consider the 3-D compressible viscous magnetohydrodynamic (MED) equations with some large potential force in bounded rigid vessel. We firstly construct the non-constant stationary solutions of the compressible viscous MED equations under suitable constitutive assumptions. Next, a critical energy identity is established to achieve a universal stability criterion of the stationary solution. In this case, the stationary solution is exponential stable for any large external potential force. Finally, we show the well-posedness of the initial boundary value problem for the compressible viscous MEAD equations with the large potential force, provided that the prescribed initial data is close to the stationary solution. It implies that the set satisfying the stability criterion is not empty. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free