Communications in Mathematical Sciences
Volume 12 (2014)
Zero dissipation limit to rarefaction wave with vacuum for one-dimensional full compressible Navier-Stokes equations
Pages: 1135 – 1154
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.
compressible fluid, Navier-Stokes equations, rarefaction wave, vacuum, zero dissipation limit
2010 Mathematics Subject Classification
35L60, 35L65, 76N15