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

2012/03/06 by Huang, Feimin, Jiang, Song, Wang, Yi
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1203.1230

Abstract

We consider the zero dissipation limit of the full compressible Navier-Stokes equations with Riemann initial data in the case of superposition of two rarefaction waves and a contact discontinuity. It is proved that for any suitably small viscosity ε and heat conductivity κ satisfying the relation \eqrefviscosity, there exists a unique global piecewise smooth solution to the compressible Navier-Stokes equations. Moreover, as the viscosity ε 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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