Communications in Mathematical Sciences

Volume 17 (2019)

Number 7

Linearized asymptotic stability of rarefaction waves for gas dynamics in thermal nonequilibrium and life span of solutions

Pages: 1795 – 1839

DOI: https://dx.doi.org/10.4310/CMS.2019.v17.n7.a3

Authors

Tao Luo (Department of Mathematics, City University of Hong Kong, Kowloon Tong, H.K.)

Hua Zhong (Department of Mathematics, City University of Hong Kong, Kowloon Tong, H.K.)

Abstract

For the one-dimensional gas flow in vibrational nonequilibrium, the linearized asymptotic stability of rarefaction waves is obtained in this paper with convergence rate, and the life-span of the solution in terms of the rarefaction wave strength is also given when the initial data are perturbations of a smooth rarefaction wave of the equilibrium of the compressible Euler equations. The main feature of the problems is that the $L^2$-norm of the perturbations may grow in time.

Keywords

thermal nonequilibrium, rarefaction wave, linearized asymptotic stability, life-span

2010 Mathematics Subject Classification

35B35, 35B40

Full Text (PDF format)

This research was supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. 11306117).

Received 5 February 2019

Accepted 4 April 2019

Published 6 January 2020