Stability of rarefaction wave for relaxed compressible Navier-Stokes equations with density-dependent viscosity

Abstract

This article shows time-asymptotic nonlinear stability of rarefaction wave to the Cauchy problem for the one-dimensional relaxed compressible Navier-Stokes equations with density-dependent viscosity. We prove that the solution to this typical system tends time-asymptotically to the rarefaction wave. For this, we technically construct the correction function Sˆ(x,t)\hat{S}\left(x,t), which means that S±{S}_{\pm } can be non-zero. The proof is accomplished by virtue of energy estimates.

Keywords

• compressible navier-stokes equations
• rarefaction wave
• correction function
• energy estimates
• 35q35
• 35q60
• 76n30
• 76w05