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# Communications in Mathematical Sciences

## Volume 12 (2014)

### Number 6

### Zero dissipation limit to rarefaction wave with vacuum for one-dimensional full compressible Navier-Stokes equations

Pages: 1135 – 1154

DOI: http://dx.doi.org/10.4310/CMS.2014.v12.n6.a6

#### Authors

#### Abstract

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.

#### Keywords

compressible fluid, Navier-Stokes equations, rarefaction wave, vacuum, zero dissipation limit

#### 2010 Mathematics Subject Classification

35L60, 35L65, 76N15