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

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

Pages: 1847 - 1868, Volume 36, Issue 4, April 2016      doi:10.3934/dcds.2016.36.1847

 
       Abstract        References        Full Text (432.1K)       Related Articles       

Hong Cai - School of Mathematical Sciences and Fujian Provincial Key Laboratory, on Mathematical Modeling and Scientific Computing, Xiamen University, Fujian, Xiamen, 361005, China (email)
Zhong Tan - School of Mathematical Sciences and Fujian Provincial Key Laboratory, on Mathematical Modeling and Scientific Computing, Xiamen University, Fujian, Xiamen, 361005, China (email)

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.

Received: March 2015;      Revised: May 2015;      Available Online: September 2015.

 References