Stability of Superposition of Viscous Contact Wave and Rarefaction Waves for Compressible Navier-Stokes System with Degenerate Heat-Conductivity and Large-Data

TL;DR

This paper proves the asymptotic stability of combined viscous contact and rarefaction waves in a one-dimensional compressible Navier-Stokes system with temperature-dependent heat conductivity, even under large initial disturbances.

Contribution

It establishes the large-time stability of superpositions of viscous contact and rarefaction waves for a degenerate heat-conductivity Navier-Stokes system with large initial data.

Findings

Asymptotic stability of wave superpositions is proven.

Stability holds under large initial perturbations.

Results apply to systems with temperature-dependent heat conductivity.

Abstract

This paper is concerned with the large-time behavior of solutions for the compressible Navier-Stokes system with degenerate heat-conductivity describing the one-dimensional motion of a viscous heat-conducting perfect polytropic gas. We proved that for the one-dimensional compressible system with temperature-dependent heat conductivity, the combination of viscous contact wave with rarefaction waves for the non-isentropic polytropic gas is asymptotically stable under large initial perturbation, provided the strength of the combination waves is suitably small.