Axisymmetric Solutions of the Euler Equations for Sub-Square Polytropic Gases

Details Axisymmetric Solutions of the Euler Equations for Sub-Square Polytropic Gases Axisymmetric Solutions of the Euler Equations for Sub-Square Polytropic Gases

1998-07-29

arxiv.org/abs/math/9807167v2

Mathematics

Analysis of PDEs

41pp, 14 figures, but 2 figures are separated from the main flow of text, they are named p4f1.1.ps and p4f1.2.ps

Scientific paper

We establish rigorously the existence of a three-parameter family of self-similar,globally bounded, and continuous weak solutions in two space dimensions to the compressible Euler equations with axisymmetry for gamma-law polytropic gases with gamma between 1 and 2, including 1. The initial data of these solutions have constant densities and outward-swirling velocities. 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.

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