Asymptotic stability of wave patterns to compressible viscous and heat-conducting gases in the half space

TL;DR

This paper investigates the long-term stability of wave patterns, including rarefaction waves and stationary solutions, in the flow of viscous, heat-conducting gases modeled by the compressible Navier-Stokes equations in a half-space setting.

Contribution

It proves the asymptotic stability of combined wave patterns for large initial disturbances in a half-space, extending previous results to more general conditions.

Findings

Rarefaction waves are asymptotically stable.

Superposition with stationary solutions remains stable.

Results hold for large initial perturbations and general adiabatic exponents.

Abstract

We study the large-time behavior of solutions to the compressible Navier-Stokes equations for a viscous and heat-conducting ideal polytropic gas in the one-dimensional half-space. A rarefaction wave and its superposition with a non-degenerate stationary solution are shown to be asymptotically stable for the outflow problem with large initial perturbation and general adiabatic exponent.