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 S ˆ (x, t) S (x, t), which means that S ± S can be non-zero. The proof is accomplished by virtue of energy estimates.