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

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.