Abstract
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.
| 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 |