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Existence and stability of entropy solutions for the hyperbolic systems of isentropic gas dynamics in Eulerian and Lagrangian coordinates

Lions, Pierre-Louis; Perthame, Benoît; Souganidis, Panagiotis E. (1996), Existence and stability of entropy solutions for the hyperbolic systems of isentropic gas dynamics in Eulerian and Lagrangian coordinates, Communications on Pure and Applied Mathematics, 49, 6, p. 599-638. http://dx.doi.org/10.1002/(SICI)1097-0312(199606)49:6<599::AID-CPA2>3.0.CO;2-5

Type
Article accepté pour publication ou publié
Date
1996
Journal name
Communications on Pure and Applied Mathematics
Volume
49
Number
6
Publisher
Wiley
Pages
599-638
Publication identifier
Metadata
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Author(s)
Lions, Pierre-Louis
Perthame, Benoît cc
Souganidis, Panagiotis E.
Abstract (EN)
We prove the existence and compactness (stability) of entropy solutions for the hyperbolic systems of conservation laws corresponding to the isentropic gas dynamics, where the pressure and density are related by a γ-law, for any γ > 1. Our results considerably extend and simplify the program initiated by DiPerna and provide a complete existence proof. Our methods are based on the compensated compactness and the kinetic formulation of systems of conservation laws.
Subjects / Keywords
isentropic gas dynamics; entropy; hyperbolic systems of conservation laws