Dynamics of Partial Differential Equations

Volume 14 (2017)

Number 4

The limit behavior of relaxation time for full compressible magnetohydrodynamic flows with Cattaneo’s law

Pages: 359 – 373

DOI: https://dx.doi.org/10.4310/DPDE.2017.v14.n4.a3


Guowei Liu (School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, China)

Xin Xu (Institute of Applied Physics and Computational Mathematics, Beijing, China)


In this paper, we discuss the system of full compressible magnetohydrodynamic equations with replacing the Fourier’s law by Cattaneo’s law in $\mathbb{R}^3$. First, local existence of solutions for general initial data and global existence of solutions for small initial data are shown. Then we obtain the uniform convergence of solutions of the relaxed system to that of the classical system when the relaxation time $\epsilon$ goes to $0$.


magnetohydrodynamic flows, Cattaneo’s law, the relaxation time, the limit behavior

2010 Mathematics Subject Classification

Primary 35B25. Secondary 76N10.

The first author is partially supported by the National Natural Science Foundation of China (No. 11231006) and (No. 11571231).

The second author is supported by Postdoctoral Science Foundation of China (No. 2017M610818).

Received 26 May 2016

Published 14 December 2017