### Abstract

Original language | English |
---|---|

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 |

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### Cite this

*Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences*,

*457*(2009), 1115-1135.

**Vortex rings in R-3 and rearrangements.** / Badiani, T V; Burton, G R.

Research output: Contribution to journal › Article

*Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences*, vol. 457, no. 2009, pp. 1115-1135.

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TY - JOUR

T1 - Vortex rings in R-3 and rearrangements

AU - Badiani, T V

AU - Burton, G R

N1 - ID number: ISI:000168646200007

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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.

M3 - Article

VL - 457

SP - 1115

EP - 1135

JO - Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences

SN - 1364-503X

IS - 2009

ER -