Kinetic invariant domains and relaxation limit from a BGK model to isentropic gas dynamics

Article type: Research Article

Authors: Berthelin, F. | Bouchut, F.

Affiliations: Département de Mathématiques, Université d'Orléans et CNRS, UMR 6628, BP 6759, 45067 Orléans cedex 2, France E‐mail: florent.berthelin@labomath.univ‐orleans.fr | Département de Mathématiques et Applications, École Normale Supérieure et CNRS, UMR 8553, 45, rue d'Ulm, 75230 Paris cedex 05, France E‐mail: Francois.Bouchut@ens.fr

Abstract: We obtain rigorously the correspondence between kinetic and macroscopic invariant domains for a vector kinetic BGK system considered in a previous paper of the authors. We establish the convergence, as the relaxation parameter tends to 0, to weak entropy solutions of isentropic gas dynamics equations.

Keywords: isentropic gas dynamics, kinetic BGK model, kinetic entropy, kinetic invariant domain, relaxation limit

Journal: Asymptotic Analysis, vol. 31, no. 2, pp. 153-176, 2002