Manuel del Pino (University of Bath)

Solutions with highly concentrated vorticity in incompressible Euler flows

Abstract:

A classical problem that traces back to Helmholtz and Kirchhoff is the understanding of the dynamics of solutions to the Euler equations of an inviscid incompressible fluid when the vorticity of the solution is initially concentrated near isolated points in 2d or vortex lines in 3d. We discuss some recent results on these solutions' existence and asymptotic behaviour. We prove 1858's conjecture by Helmholtz on vortex ring leapfrogging dynamics. This is research in collaboration with J. Dávila, A. Fernández, M. Musso, S. Parmeshwar and J. Wei.