Nonlinear Stability for the Superposition of Viscous Contact Wave and Rarefaction Waves to Non-isentropic Compressible Navier-Stokes System with General Initial Perturbations

Abstract

In this paper, the large time behavior of the solutions for the Cauchy problem to the one-dimensional compressible Navier-Stokes system with the motion of a viscous heat-conducting perfect polytropic gas is investigated.Our result shows that the combination of a viscous contact wave with rarefaction waves is asymptotically stable, when the large initial disturbance of the density, velocity and temperature belong to $H^{1}(\mathbb{R})$, $L^{2}(\mathbb{R})\cap L^{4}(\mathbb{R})$ and $L^{2}(\mathbb{R})$, provided the strength of the combination waves is suitably small. In addition, the initial disturbance on the derivation of velocity and temperature belong to $L^{2}(\mathbb{R})$ can be arbitrarily large.