Axisymmetric solutions of the Euler equations for polytropic gases

Tong Zhang, Yuxi Zheng

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)253-279
Number of pages27
JournalArchive for Rational Mechanics and Analysis
Issue number3
StatePublished - Jul 16 1998

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering


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