Stability and decay rate of viscous contact wave to one-dimensional compressible Navier-Stokes equations

Abstract

This paper studies the large-time asymptotic stability and optimal time-decay rate of viscous contact wave to one-dimensional compressible Navier–Stokes equations. We prove that one-dimensional compressible Navier–Stokes equations are asymptotically stable for viscous contact wave with arbitrarily large strength, under large initial perturbations. The time optimal decay rate of viscous contact wave is also obtained under the small initial perturbations. In the proof, the Lagrange transform is used to cancel the convection terms, which are difficult to estimate due to the lower spatial derivatives compared with the diffusion terms.