Asymptotic stability of stationary solutions for magnetohydrodynamic equations

Zhong Tan; Leilei Tong

doi:10.3934/dcds.2017146

Article Contents

2017, Volume 37, Issue 6: 3435-3465. Doi: 10.3934/dcds.2017146

This issue Previous Article Global existence and low Mach number limit to a 3D compressible micropolar fluids model in a bounded domain Next Article Global asymptotic stability of pushed traveling fronts for monostable delayed reaction-diffusion equations

Asymptotic stability of stationary solutions for magnetohydrodynamic equations

Zhong Tan and
Leilei Tong

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: May 2017

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

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Abstract

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 L^p-L^q decay estimates and the higher-order energy estimates.

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Mathematics Subject Classification: Primary: 35B35, 35M31; Secondary: 35Q60, 35Q35.

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