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From kinetic equations to multidimensional isentropic gas dynamics before shocks. (English) Zbl 1130.35090

This article is devoted to the proof of the hydrodynamical limit from kinetic 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.

MSC:

35L65 Hyperbolic conservation laws
35F20 Nonlinear first-order PDEs
82C40 Kinetic theory of gases in time-dependent statistical mechanics
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