On the global stability of contact discontinuity for compressible Navier-Stokes equations (Q2569617)

Summary: The asymptotic behavior of the solutions toward the contact discontinuity for the one-dimensional compressible Navier-Stokes equations with a free boundary is investigated. It is shown that the viscous contact discontinuity introduced by \textit{F. Huang, A. Matsumura} and \textit{X. Shi} [Osaka J. Math. 41, No. 1, 193--210 (2004; Zbl 1062.35066)] is asymptotic stable with arbitrarily large initial perturbation if the adiabatic exponent \(g\) is near \(1\). The case the asymptotic state is given by a combination of viscous contact discontinuity and the rarefaction wave is further investigated. Both the strength of rarefaction wave and the initial perturbation can be arbitrarily large.