Vanishing viscosity of isentropic Navier-Stokes equations for interacting shocks

Abstract

We study the vanishing viscosity of the Navier-Stokes equations for interacting shocks. Given an entropy solution to p -system which consists of two different families of shocks interacting at some positive time, we show that such entropy solution is the vanishing viscosity limit of a family of global smooth solutions to the isentropic Navier-Stokes equations. The key point of the proofs is to derive the estimates separately before and after the interaction time and connect the incoming and outgoing viscous shock profiles.