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



Ming-Jie Li (College of Science, Minzu University of China, Beijing, China)

Teng Wang (Institute of Applied Mathematics, AMSS, Beijing, China)


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

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