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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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##### References:
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