Mestrandos

Workshop on Pdes 2022 - Del Pino

Dynamics of concentrated vorticities in 2d and 3d Euler flows

Prof. Manuel Del Pino
The University of Bath

Date: 16th February 09:00 am - 09:45 am (UTC -3) Link: PPGM/UFSCar Youtube channel

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 the existence and asymptotic behaviour of these solutions. We describe, with precise asymptotics, interacting vortices, and travelling helices. We rigorously establish the law of motion of ”leapfrogging vortex rings”, originally conjectured by Helmholtz in 1858.