### Abstract

We consider a Riemann-type initial value problem for the compressible and polytropic two-dimensional Euler equations. The initial states are such that the flows have constant densities, and all fluid particles rotate clockwise (or counter clockwise) around the origin in circles with a constant speed. The equations are reduced to a system of ordinary differential equations for self-similar and axisymmetric solutions. We have established the existence of a two-parameter family of such solutions. All these solutions are globally bounded and continuous, have finite local energy and vorticity with finite boundary values at infinity. A one-parameter family of such solutions is in explicit form. The incompressible Euler equations with similar initial data are also considered.

Original language | English (US) |
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Pages (from-to) | 145-147 |

Number of pages | 3 |

Journal | ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik |

Volume | 76 |

Issue number | SUPPL. 2 |

State | Published - Dec 1 1996 |

### All Science Journal Classification (ASJC) codes

- Computational Mechanics
- Applied Mathematics

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## Cite this

*ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik*,

*76*(SUPPL. 2), 145-147.