Communications in Mathematical Sciences
Volume 17 (2019)
Linearized asymptotic stability of rarefaction waves for gas dynamics in thermal nonequilibrium and life span of solutions
Pages: 1795 – 1839
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.
thermal nonequilibrium, rarefaction wave, linearized asymptotic stability, life-span
2010 Mathematics Subject Classification
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