Stratified weak solutions of the 1-D Lagrangian Euler equations are viscosity solutions

Abstract

Recently, a class of weak solutions called "stratified" solutions have been introduced for systems of conservation laws in 1d which have a linear degenerate field and a "good symmetrizer," like the Euler system of entropic gaz dynamics ([5], [16]). These solutions can have an unbounded local variation and they generalize the "large-amplitude oscillatory solutions" previously studied by W.E, A. Heibig, and D. Serre ([13], [7], [22]). In this paper we show that, in the case of the Lagragian Euler equations of gaz dynamics, these stratified solutions are the limit of solutions of a vanishing viscosity perturbation of the system.