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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Additional information
(Accepted October 29, 1996)
Rights and permissions
About this article
Cite this article
Zhang, T., Zheng, Y. Axisymmetric Solutions of the Euler Equations for Polytropic Gases. Arch Rational Mech Anal 142, 253–279 (1998). https://doi.org/10.1007/s002050050092
Issue Date:
DOI: https://doi.org/10.1007/s002050050092