From Kinetic Equations to Multidimensional Isentropic Gas Dynamics Before Shocks

This article is devoted to the proof of the hydrodynamical limit from kinetic equations (including BGK-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 velocity distributions for kinetic functions is needed. The case of the Saint–Venant system with topography (where a source term is added) is included.