Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Asymptotic stability of stationary solutions for magnetohydrodynamic equations

Pages: 3435 - 3465, Volume 37, Issue 6, June 2017      doi:10.3934/dcds.2017146

       Abstract        References        Full Text (533.6K)       Related Articles       

Zhong Tan - School of Mathematical Sciences and Fujian Provincial Key Laboratory, on Mathematical Modeling and Scientific Computing, Xiamen University, Xiamen, 361005, China (email)
Leilei Tong - School of Mathematical Science and Fujian Provincial Key Laboratory, on Mathematical Modeling & High Performance Scientific Computing, Xiamen University, Xiamen 361005, China (email)

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.

Keywords:  MHD equations, global solutions, stability, energy method, time decay rate.
Mathematics Subject Classification:  Primary: 35B35, 35M31; Secondary: 35Q60, 35Q35.

Received: July 2015;      Revised: January 2017;      Available Online: February 2017.