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Existence and stability of entropy solutions for the hyperbolic systems of isentropic gas dynamics in Eulerian and Lagrangian coordinates. (English) Zbl 0853.76077
Summary: 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 \(\gamma\)-law, for any \(\gamma>1\). 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.

MSC:
76N15 Gas dynamics, general
35Q35 PDEs in connection with fluid mechanics
35L65 Hyperbolic conservation laws
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