Asymptotic stability of viscous contact wave and rarefaction waves for the system of heat-conductive ideal gas without viscosity

TL;DR

This paper proves the global existence and asymptotic stability of solutions to the heat-conductive ideal gas system without viscosity, showing convergence to viscous contact and rarefaction waves under small initial perturbations.

Contribution

It extends previous results by establishing stability and convergence for the non-viscous heat-conductive ideal gas system, which was not previously addressed.

Findings

Global-in-time solutions exist for small initial perturbations.

Solutions asymptotically tend to viscous contact and rarefaction waves.

Results extend stability analysis to non-viscous heat-conductive gases.

Abstract

This paper is concerned with the Cauchy problem of heat-conductive ideal gas without viscosity. We show that, for the non-viscous case, if the strengths of the wave patterns and the initial perturbation are suitably small, the unique global-in-time solution exists and asymptotically tends toward the corresponding the viscous contact wave or the composition of a viscous contact wave with rarefaction waves determined by the initial condition, which extended the results by Huang-Li-Matsumura[13], where they treated the viscous and heat-conductive ideal gas.