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Existence and isoperimetric characterization of steady spherical vortex rings in a uniform flow in RN

Published online by Cambridge University Press:  12 July 2007

Geoffrey R. Burton  and
Luca Preciso
Geoffrey R. Burton
Affiliation:
Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, UK ([email protected])
Luca Preciso
Affiliation:
Department of Pure and Applied Mathematics, University of Padova, via G. Belzoni 7, 35131 Padova, Italy ([email protected])
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Abstract

We study a boundary-value problem for a particular semilinear elliptic equation on Rn (n ≥ 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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 134 , Issue 3 , June 2004 , pp. 449 - 476
Copyright
Copyright © Royal Society of Edinburgh 2004

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