Berthelin, F.; Vasseur, A. From kinetic equations to multidimensional isentropic gas dynamics before shocks. (English) Zbl 1130.35090 SIAM J. Math. Anal. 36, No. 6, 1807-1835 (2005). 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. Reviewer: Oleg Dementiev (Chelyabinsk) Cited in 2 ReviewsCited in 36 Documents MSC: 35L65 Hyperbolic conservation laws 35F20 Nonlinear first-order PDEs 82C40 Kinetic theory of gases in time-dependent statistical mechanics Keywords:hydrodynamic limit; entropy method; isentropic gas dynamics; Saint-Venant system PDFBibTeX XMLCite \textit{F. Berthelin} and \textit{A. Vasseur}, SIAM J. Math. Anal. 36, No. 6, 1807--1835 (2005; Zbl 1130.35090) Full Text: DOI