Asymptotic stability of viscous contact discontinuity to an inflow problem for compressible Navier–Stokes equations

This paper is concerned with an initial-boundary value problem for one-dimensional full compressible Navier–Stokes equations with inflow boundary conditions in the half space R+=(0,+∞)R+=(0,+∞). The asymptotic stability of viscous contact discontinuity is established under the conditions that the initial perturbations and the strength of contact discontinuity are suitably small. Compared with the free-boundary and the initial value problems, the inflow problem is more complicated due to the additional boundary effects and the different structure of viscous contact discontinuity. The proofs are given by the elementary energy method.