Self-similar solutions of the Euler equations with spherical symmetry |
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Authors: | Chen-Chang Peng Wen-Ching Lien |
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Institution: | 1. Department of Applied Mathematics, National Chiayi University, No. 300, Xuefu Rd., Chiayi City, 60004, Taiwan;2. Department of Mathematics, National Cheng Kung University, No. 1, Dasyue Rd., Tainan City, 70101, Taiwan |
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Abstract: | We consider self-similar flows arising from the uniform expansion of a spherical piston and preceded by a shock wave front. With appropriate boundary conditions imposed on the piston surface and the spherical shock, the isentropic compressible Euler system is transformed into a nonlinear ODE system. We formulate the problem in a simple form in order to present the analytic proof of the global existence of positive smooth solutions. |
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Keywords: | 34B 35L 76N |
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