Global stability of wave patterns for compressible navier-stokes system with free boundary

In this article, we investigate the global stability of the wave patterns with the superposition of viscous contact wave and rarefaction wave for the one-dimensional compressible Navier-Stokes equations with a free boundary. It is shown that for the ideal polytropic gas, the superposition of the viscous contact wave with rarefaction wave is nonlinearly stable for the free boundary problem under the large initial perturbations for any γ > 1 with γ being the adiabatic exponent provided that the wave strength is suitably small.