# American Institute of Mathematical Sciences

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Global existence and low Mach number limit to a 3D compressible micropolar fluids model in a bounded domain
June  2017, 37(6): 3435-3465. doi: 10.3934/dcds.2017146

## Asymptotic stability of stationary solutions for magnetohydrodynamic equations

 School of Mathematical Science and Fujian Provincial Key Laboratory, on Mathematical Modeling & High Performance Scientific Computing, Xiamen University, Xiamen 361005, China

Received  July 2015 Revised  January 2017 Published  February 2017

Fund Project: Supported by the National Natural Science Foundation of China (Grant No. 11271305,11531010) and the Fundamental Research Funds for Xiamen University (No. 201412G004)

In this paper, we are concerned with the compressible magnetohydrodynamic equations with Coulomb force in three-dimensional space. We show the asymptotic stability of solutions to the Cauchy problem near the non-constant equilibrium state provided that the initial perturbation is sufficiently small. Moreover, the convergence rates are obtained by combining the linear Lp-Lq decay estimates and the higher-order energy estimates.

Citation: Zhong Tan, Leilei Tong. Asymptotic stability of stationary solutions for magnetohydrodynamic equations. Discrete & Continuous Dynamical Systems - A, 2017, 37 (6) : 3435-3465. doi: 10.3934/dcds.2017146
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