Vanishing Viscosity Limit of the Compressible Navier-Stokes Equations for Solutions to a Riemann Problem

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Original languageEnglish
Pages (from-to)379-413
Journal / PublicationArchive for Rational Mechanics and Analysis
Volume203
Issue number2
Publication statusPublished - Feb 2012

Abstract

We study the vanishing viscosity limit of the compressible Navier-Stokes equations to the Riemann solution of the Euler equations that consists of the superposition of a shock wave and a rarefaction wave. In particular, it is shown that there exists a family of smooth solutions to the compressible Navier-Stokes equations that converges to the Riemann solution away from the initial and shock layers at a rate in terms of the viscosity and the heat conductivity coefficients. This gives the first mathematical justification of this limit for the Navier-Stokes equations to the Riemann solution that contains these two typical nonlinear hyperbolic waves. © 2011 Springer-Verlag.