Entropy boundary layers

Abstract

We consider the Euler system of compressible and entropic gaz dynamics in a bounded open domain with wall boundary condition. We prove the existence and the stability of families of solutions which correspond to a ground state plus a large entropy boundary layer. The ground state is a solution of the Euler system which satisfies some explicit additional conditions on the boundary. These conditions are used in a reduction of the system. We construct BKW expansions at all order. The profile problems are linear thanks to a transparency property. We prove the stability of these expansions by proving epsilon-conormal estimates for a characteristic boundary value problem.