In this talk, we discuss recent developments concerning the motion of concentrated vortex rings. In particular, we outline the proof that, in the appropriate asymptotic regime, two concentrated coaxial vortex rings separated by a small distance exhibit the so-called leapfrogging motion. This highly singular regime lies beyond the scope of the standard tools of vorticity confinement. We introduce a new method to establish the persistence of mass concentration, and then implement a refined iterative scheme, combined with sharper estimates, to control the growth of the vorticity support. The choice of the asymptotic regime will be discussed, along with the technical limitations of our result.
De Geoffrey Vallis
De Luca Melzi
De Beatrice Pelloni
