On leapfrogging vortex rings for the Euler equations

Vortrag von Dr. Lars Eric Hientzsch

Sprecher eingeladen von: Prof. Dr. Klaus Widmayer

Datum: 26.02.26  Zeit: 16.15 - 18.00  Raum: Y27H35/36

In 1858, Helmholtz conjectured that coaxial vortex rings in 3D inviscid fluids can exhibit the "leapfrogging" dynamics, where rings repeatedly pass through one another. While well-documented experimentally, this phenomenon involves singular interactions that are difficult to capture analytically. In this talk, we present a rigorous justification of these dynamics for the 3D incompressible Euler equations. We consider a general class of initial data corresponding to N sharply concentrated coaxial vortex rings and prove that the leapfrogging motion persists on a logarithmic time scale. The core of the analysis requires new estimates to propagate the concentration of vorticity despite the singular mutual interactions required for the phenomenon to occur. 

Joint work with M. Donati, C. Lacave, and E. Miot.