Abstract:
This article is devoted to the proof of the hydrodynamical limit
from kinetic equations (including B.G.K. like equations) to
multidimensional isentropic gas dynamics. It is based on a
relative entropy method, hence the derivation is valid only before
shocks appear on the limit system solution. However, no a priori
knowledge on high velocities distributions for kinetic functions
is needed. The case of the Saint-Venant system with topography
(where a source term is added) is included.