Time periodic solutions to the three--dimensional equations of compressible magnetohydrodynamic flows

Hong  Cai; Zhong  Tan

doi:10.3934/dcds.2016.36.1847

Article Contents

2016, Volume 36, Issue 4: 1847-1868. Doi: 10.3934/dcds.2016.36.1847

This issue Previous Article Stability of variational eigenvalues for the fractional $p-$Laplacian Next Article Sharp decay estimates and smoothness for solutions to nonlocal semilinear equations

Time periodic solutions to the three--dimensional equations of compressible magnetohydrodynamic flows

Hong Cai^1, and
Zhong Tan^1,

1.
School of Mathematical Sciences and Fujian Provincial Key Laboratory, on Mathematical Modeling and Scientific Computing, Xiamen University, Fujian, Xiamen, 361005

Received: March 2015

Revised: May 2015

Published: May 2017

Abstract / Introduction Related Papers Cited by

Abstract

In this paper, the compressible magnetohydrodynamic system with some smallness and symmetry assumptions on the time periodic external force is considered in $\mathbb{R}^3$. Based on the uniform estimates and the topological degree theory, we prove the existence of a time periodic solution in a bounded domain. Then by a limiting process, the result in the whole space $\mathbb{R}^3$ is obtained.

Keywords:

$3D$ Compressible magnetohydrodynamic equations,
time periodic solution,
uniform estimates,
topological degree theory.

Mathematics Subject Classification: Primary: 35Q35; Secondary: 35B10, 76N10.

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