### Abstract

Original language | English |
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Pages (from-to) | 449-476 |

Number of pages | 28 |

Journal | Proceedings of the Royal Society of Edinburgh Section A - Mathematics |

Volume | 134 |

Publication status | Published - 2004 |

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### Cite this

**Existence and isoperimetric characterization of steady spherical vortex rings in a uniform flow in R-N.** / Burton, G R; Preciso, L.

Research output: Contribution to journal › Article

*Proceedings of the Royal Society of Edinburgh Section A - Mathematics*, vol. 134, pp. 449-476.

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TY - JOUR

T1 - Existence and isoperimetric characterization of steady spherical vortex rings in a uniform flow in R-N

AU - Burton, G R

AU - Preciso, L

N1 - ID number: ISI:000222878500002

PY - 2004

Y1 - 2004

N2 - We study a boundary-value problem for a particular semilinear elliptic equation on R-n (n greater than or equal to 2), whose solutions represent generalized stream functions for steady axisymmetric ideal fluid flows. Solutions are shown to exist that generalize those already known in dimensions 2 and 3. An isoperimetric characterization is given for our solutions, which represent generalized spherical vortex-rings. As a corollary, a sharp Sobolev-type inequality is obtained.

AB - We study a boundary-value problem for a particular semilinear elliptic equation on R-n (n greater than or equal to 2), whose solutions represent generalized stream functions for steady axisymmetric ideal fluid flows. Solutions are shown to exist that generalize those already known in dimensions 2 and 3. An isoperimetric characterization is given for our solutions, which represent generalized spherical vortex-rings. As a corollary, a sharp Sobolev-type inequality is obtained.

M3 - Article

VL - 134

SP - 449

EP - 476

JO - Proceedings of the Royal Society of Edinburgh Section A - Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A - Mathematics

SN - 0308-2105

ER -