Existence and isoperimetric characterization of steady spherical vortex rings in a uniform flow in RN
Published online by Cambridge University Press: 12 July 2007
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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