## Abstract

We study the existence of steady axisymmetric vortex rings in an ideal fluid. A functional, comprising a linear combination of kinetic energy and impulse, is to be maximized subject to the constraint that a quantity related to vorticity belongs to a set of rearrangements of a given function. Generalized solutions of a quite specific type are shown to exist, arising as extreme points of a convex extended constraint set. In the case when the given function is the indicator of a set of finite measure, the existence of proper maximizers and local maximizers is demonstrated.

Original language | English |
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Pages (from-to) | 1115-1135 |

Number of pages | 21 |

Journal | Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences |

Volume | 457 |

Issue number | 2009 |

Publication status | Published - 2001 |