The stability of strong viscous contact discontinutiy to an inflow problem for full compressible Navier-Stokes equations

Abstract

This paper is concerned with nonlinear stability of viscous contact discontinuity to inflow problem for the one-dimensional full compressible Navier-Stokes equations with different ends in half space $[0,\infty)$. For the case when the local stability of the contact discontinuities was first studied by \cite{X},later generalized by \cite{LX}, local stability of weak viscous contact discontinuity is well-established by \cite{HMS,HMX,HXY,HZ,HLM2009}, but for the global stability of inflow gas with big oscillation ends $(|\theta_+-\theta_-|>1\ and \ |\rho_+-\rho_-|>1)$, fewer results have been obtained excluding zero dissipation \cite{MaSX} or $\gamma\to 1$ gas see \cite{HH}. Our main purpose is to deduce the corresponding nonlinear stability result with the two different ends by exploiting the elementary energy method. As a first step towards this goal, we will show in this paper that with a certain class of big perturbation which can allow $|\theta_--\theta_+|>1$ and $|\rho_--\rho_+|>1$ ,the global stability result holds.