Stability of viscous contact wave for compressible Navier-Stokes equations with a large initial perturbation

Abstract

The viscous contact wave for the compressible Navier-Stokes equations has recently been shown to be asymptotically stable provided that all the L2 norms of initial perturbations, their derivatives and/or anti-derivatives are small. The main purpose of this paper is to study the asymptotic stability and convergence rate of the viscous contact wave with a large initial perturbation. For this purpose, we introduce a positive number l in the construction of a smooth approximation of the contact discontinuity for the compressible Euler equations and then we make the quantity l to be sufficiently large in order to control the growth induced by the nonlinearity of the system and the interaction of waves from different families. This makes for us to estimate the L2 norms of the solution and its derivative for perturbation system without assuming that L2 norms of the anti-derivatives and the derivatives of initial perturbations are small.