M. Del Pino | Dynamics of concentrated vorticities in 2d and 3d Euler flows
Channel: EIMI, PDMI RAS and Chebyshev Laboratory
Date: 01/08/2022

O.A. Ladyzhenskaya centennial conference on PDE’s, St. Petersburg, July 16 – July 22, 2022
Manuel Del Pino (University of Bath) 
Dynamics of concentrated vorticities in 2d and 3d Euler flows

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 behavior. We describe, with precise asymptotics, interacting vortices, and traveling helices. We rigorously establish the law of motion of ”leapfrogging vortex rings”, initially conjectured by Helmholtz in 1858.