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Axisymmetric solutions of the Euler system for the Chaplygin gas. (Chinese. English translation) Zbl 1240.35354

Chin. Ann. Math., Ser. A 32, No. 2, 193-204 (2011); translation in Chin. J. Contemp. Math. 32, No. 2, 171-182 (2011).
Summary: In this paper, a three-parameter family of self-similar weak solutions is constructed in a two-dimensional space for all positive time to the axisymmetric Euler equations for the Chaplygin gas. Under the self-similar and axisymmetry assumptions, the equations are reduced to a system of three ordinary differential equations with boundary value at infinity, from which the detailed structures of solutions as well as their existence are obtained. Different from polytropic gas, the Euler equations for the Chaplygin gas are fully linear degenerate. Discontinuities exist even though the velocity of radially direction is positive. These solutions exhibit some phenomena, such as black hole, expansion and explosive expansion, in the evolution of universe.

MSC:

35L65 Hyperbolic conservation laws
35L67 Shocks and singularities for hyperbolic equations
76L05 Shock waves and blast waves in fluid mechanics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
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