Steady Vortex Rings in a Uniform Flow and Rearrangements of a Function

Abstract

We prove the existence of steady vortex rings of an ideal fluid in a uniform flow. We use an approach based on a variational principle for the vorticity. We show equally that the maximiser (which represents a quantity related to the vorticity) of a functional related to kinetic energy and the impulse over a class of rearrangements of a prescribed function $$\zeta _0$$, is in fact a rearrangement of $$\zeta _0$$.