Vortex rings in R-3 and rearrangements

We study the existence of steady axisymmetric vortex rings in an ideal fluid. A functional, comprising a linear combination of kinetic energy and impulse, is to be maximized subject to the constraint that a quantity related to vorticity belongs to a set of rearrangements of a given function. Generalized solutions of a quite specific type are shown to exist, arising as extreme points of a convex extended constraint set. In the case when the given function is the indicator of a set of finite measure, the existence of proper maximizers and local maximizers is demonstrated.