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 $(|{\theta }_{+}-{\theta }_{-}|>1and|{\rho }_{+}-{\rho }_{-}|>1)$, 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.

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. arXiv admin note: substantial text overlap with arXiv:1407.5502