Stability of a strong viscous contact discontinuity in a free boundary problem for compressible Navier–Stokes equations

Abstract

In this study, we consider the nonlinear stability of a strong viscous contact discontinuity in a free boundary problem for the one-dimensional, full compressible Navier–Stokes equations in half space [0,∞). For the local stability of contact discontinuities, the local stability of a weak viscous contact discontinuity is well established, but for the global stability of an impermeable gas, fewer strong nonlinear wave stability results have been obtained, excluding zero dissipation or a γ→1 gas. Thus, our main aim is to determine the corresponding nonlinear stability result using the elementary energy method. For a certain class of large perturbation, we show that the global stability result can be obtained for a strong viscous contact discontinuity in Navier–Stokes equations.