Stability of planar rarefaction waves under general viscosity perturbation of the isentropic Euler system

Abstract

We consider the vanishing viscosity limit for a model of a general non-Newtonian compressible fluid in $R^d$, $d=2,3$. We suppose that the initial data approach a profile determined by the Riemann data generating a planar rarefaction wave for the isentropic Euler system. Under these circumstances the associated sequence of dissipative solutions approaches the corresponding rarefaction wave strongly in the energy norm in the vanishing viscosity limit. The result covers the particular case of a linearly viscous fluid governed by the Navier–Stokes system.