Entropy boundary layers
Analysis of PDEs
2007-05-23 v1
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.
Cite
@article{arxiv.math/0511564,
title = {Entropy boundary layers},
author = {Franck Sueur},
journal= {arXiv preprint arXiv:math/0511564},
year = {2007}
}