From kinetic equations to multidimensional isentropic gas dynamics before shocks


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.
 


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