Stability of rarefaction wave for the compressible non-isentropic Navier-Stokes-Maxwell equations

Huancheng Yao; Haiyan Yin; Changjiang Zhu

doi:10.3934/cpaa.2021021

Article Contents

2021, Volume 20, Issue 3: 1297-1317. Doi: 10.3934/cpaa.2021021

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Stability of rarefaction wave for the compressible non-isentropic Navier-Stokes-Maxwell equations

1.
School of Mathematics, South China University of Technology, Guangzhou 510641, China
2.
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China

^* Corresponding author
^* Corresponding author

Received: October 31, 2020

Revised: November 30, 2020

Early access: February 2021

Published: March 2021

Huancheng Yao and Changjiang Zhu were supported by the National Natural Science Foundation of China #11771150, 11831003, 11926346 and Guangdong Basic and Applied Basic Research Foundation #2020B1515310015. Haiyan Yin was supported by the National Natural Science Foundation of China #12071163, 11601165 and the Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao University #ZQN-PY602

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Abstract

We study the large-time asymptotic behavior of solutions toward the rarefaction wave of the compressible non-isentropic Navier-Stokes equations coupling with Maxwell equations under some small perturbations of initial data and also under the assumption that the dielectric constant is bounded. For that, the dissipative structure of this hyperbolic-parabolic system is studied to include the effect of the electromagnetic field into the viscous fluid and turns out to be more complicated than that in the simpler compressible Navier-Stokes system. The proof of the main result is based on the elementary $ L^2 $ energy methods.

Keywords:

Compressible non-isentropic Navier-Stokes-Maxwell equations,
rarefaction wave,
asymptotic behavior,
electromagnetic field,
dielectric constant.

Mathematics Subject Classification: Primary: 35Q30, 76N06, 76N30; Secondary: 35Q61.

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