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.