Axisymmetric Solutions of the Euler Equations for Polytropic Gases |
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Authors: | Tong Zhang Yuxi Zheng |
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Institution: | (1) Institute of Mathematics, Academia Sinica, Beijing, China, CN;(2) Department of Mathematics, Indiana University, Bloomington, Indiana 47405, USA, US |
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Abstract: | We construct rigorously a three‐parameter family of self‐similar, globally bounded, and continuous weak solutions in two space
dimensions for all positive time to the Euler equations with axisymmetry for polytropic gases with a quadratic pressure‐density
law. We use the axisymmetry and self‐similarity assumptions to reduce the equations to a system of three ordinary differential
equations, from which we obtain detailed structures of solutions besides their existence. These solutions exhibit familiar
structures seen in hurricanes and tornadoes. They all have finite local energy and vorticity with well‐defined initial and
boundary values. These solutions include the one‐parameter family of explicit solutions reported in a recent article of ours.
(Accepted October 29, 1996) |
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Keywords: | |
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