Stability of contact discontinuity for an isentropic viscosity system with Chaplygin gas

This paper is devoted to studying the large-time behavior of solutions for an isentropic viscosity system with Chaplygin gas. Since all the characteristic fields of the corresponding inviscid Euler equations are linearly degenerate, the classical Riemann solutions only contain contact discontinuities. It is proved that for the isentropic viscosity system with Chaplygin gas, the viscous contact wave which approximates the corresponding contact discontinuity is asymptotically stable. The proof is given by elementary energy methods without anti-derivative technique.

Keywords

stability, viscous contact wave, isentropic viscosity system, Chaplygin gas

2010 Mathematics Subject Classification

35B40, 35B45, 76N10, 76Nxx

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The research of Jinjing Liu was supported by National Natural Science Foundation of China grant 12261099, 11801444. The research of Meichen Hou was supported by Natural Science Basic Research Program of Shaanxi (Program No. 2021JQ-428) and partially supported by Scientific Research Program of Shaanxi Provincial Department of Education (Program No. 22JK0582).

Received 6 April 2022

Received revised 24 November 2022

Accepted 3 December 2022

Published 22 September 2023