Axisymmetric solutions of the Chaplygin gas for initial negative radial velocity |
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| Authors: | GUO Li-hui SHENG Wan-cheng |
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| Institution: | 1. Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200444, P. R. China;College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, P. R. China
2. Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200444, P. R. China |
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| Abstract: | In this paper, a three-parameter family of self-similar and weak solutions are constructed rigorously in two space dimensions for all positive time to the Euler equations with axisymmetric and radial negative initial velocity for the Chaplygin gas. Under the axisymmetry and self-similar assumptions, the equations are reduced to a system of three ordinary differential equations, from which we obtain structures of solutions besides their existence. The solutions exhibit some phenomena, such as formation and evolution of black hole, expansion and explosive expansion, in the evolution of universe. |
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| Keywords: | Chaplygin gas axisymmetric concentration |
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