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Existence and stability of entropy solutions for the hyperbolic systems of isentropic gas dynamics in Eulerian and Lagrangian coordinates
Author(s) -
Lions PierreLouis,
Perthame Benoît,
Souganidis Panagiotis E.
Publication year - 1996
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/(sici)1097-0312(199606)49:6<599::aid-cpa2>3.0.co;2-5
Subject(s) - isentropic process , conservation law , compact space , mathematics , gas dynamics , eulerian path , entropy (arrow of time) , lagrangian , lagrangian and eulerian specification of the flow field , stability (learning theory) , mathematical analysis , kinetic energy , classical mechanics , mechanics , thermodynamics , physics , machine learning , computer science
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. © 1996 John Wiley & Sons, Inc.