Entropy boundary layers

Article type: Research Article

Authors: Sueur, Franck

Affiliations: Laboratoire d'Analyse, de Topologie et de Probabilité, Centre de Mathématiques et d'Informatique, 39, rue F. Joliot Curie, 13453 Marseille Cedex 13, France E-mail: fsueur@cmi.univ-mrs.fr

Abstract: We consider the Euler system of compressible and entropic gaz dynamics in a bounded open domain of $\mathbb {R}$d 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 ε-conormal estimates for a characteristic boundary value problem.

Journal: Asymptotic Analysis, vol. 49, no. 1-2, pp. 109-171, 2006