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Global solutions to a class of two-dimensional Riemann problems for the Euler equations with a general equation of state. (English) Zbl 1435.35246

The author considers the Riemann problem for the isentropic Euler equations with two spatial dimensions. The initial data are set in the azimuthal variable. The system is self-similar, so it is reduced to two self-similar dimensions. The system is studied, with solution decomposed into simple waves of different kind. Existence and uniqueness of a classical global solution is proved.

MSC:

35L65 Hyperbolic conservation laws
35L67 Shocks and singularities for hyperbolic equations
35C06 Self-similar solutions to PDEs
35L45 Initial value problems for first-order hyperbolic systems
35Q31 Euler equations
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