Communications in Information and Systems

Volume 13 (2013)

Number 2

Special Issue in Honor of Marshall Slemrod: Part 2 of 4

Zero dissipation limit of full compressible Navier-Stokes equations with a Riemann initial data

Pages: 211 – 246

DOI: https://dx.doi.org/10.4310/CIS.2013.v13.n2.a5

Authors

Feimin Huang (Institute of Applied Mathematics, AMSS, Chinese Academy of Sciences, Beijing, China)

Song Jiang (Institute of Applied Physics and Computational Mathematics, Beijing, China)

Yi Wang (Institute of Applied Mathematics, AMSS, Chinese Academy of Sciences, Beijing, China)

Abstract

We consider the zero dissipation limit of the full compressible Navier-Stokes equations with a Riemann initial data for the superposition of two rarefaction waves and a contact discontinuity. It is proved that for any suitably small viscosity $\epsilon$ and heat conductivity $\kappa$ satisfying the relation (1.3), there exists a unique global piecewise smooth solution to the compressible Navier-Stokes equations. Moreover, as the viscosity $\epsilon$ tends to zero, the Navier-Stokes solution converges uniformly to the Riemann solution of superposition of two rarefaction waves and a contact discontinuity to the corresponding Euler equations with the same Riemann initial data away from the initial line $t = 0$ and the contact discontinuity located at $x = 0$.

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Published 3 June 2014