ZERO DISSIPATION LIMIT TO RAREFACTION WAVE WITH VACUUM FOR ONE-DIMENSIONAL FULL COMPRESSIBLE NAVIER-STOKES EQUATIONS

摘要

We study the zero dissipation limit of the full compressible Navier-Stokes equations to a rarefaction wave which connects to vacuum at one side. It is shown that there exists a family of smooth solutions to the full compressible Navier-Stokes equations converging to the rarefaction wave with vacuum away from the initial layers at a uniform rate as the viscosity and the heat conduction coefficient tend to zero. Our method of proof consists of a scaling argument and elementary energy- analysis based on the underlying wave structure.