Global stability of viscous contact wave for 1-D compressible Navier–Stokes equations

Abstract

The viscous contact waves for one-dimensional compressible Navier–Stokes equations has recently been shown to be asymptotically stable. The stability results are called local stability or global stability depending on whether the norms of initial perturbations are small or not. Up to now, local stability results toward viscous contact waves of compressible Navier–Stokes equations have been well established (see Huang et al., 2006, 2008, 2009 [9,10,7]), but there are few results for the global stability in the case of Cauchy problem which is the purpose of this paper. The proof is based on an elementary energy method using an inequality concerning the heat kernel (see Lemma 1 of Huang et al., 2010 [7]).