Abstract:
We consider a kinetic BGK model relaxing to isentropic
gas dynamics previously introduced by the authors, but with Dirichlet boundary
condition on the incoming velocities. We pass to the limit as the
relaxation parameter tends to zero by compensated compactness inside the
domain, and obtain that the limit satisfies entropy inequalities on the
boundary involving weak traces of entropy fluxes. Our method is very general
and could be applied to any entropy satisfying BGK model as soon as we
have strong compactness of the macroscopic variables inside the domain.