Juan Dávila

University of Bath

Leapfrogging vortex rings and other solutions with concentrated vorticity for the Euler equations

We will present a construction of solutions to the 3D incompressible Euler equations displaying leapfrogging vortex rings. These solutions have vorticity highly concentrated near two rings that travel together and rotate around each other, a phenomenon predicted by Helmholtz (1858). We will also discuss other solutions with highly concentrated vorticity that desingularize point vortices in 2D and helices in 3D.

This is joint work with Manuel del Pino (U. Bath), Monica Musso (U. Bath) and Juncheng Wei (UBC).