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 behavior of these solutions. We describe, with precise asymptotics, interacting vortices, and traveling helices. We rigorously establish the law of motion of ‘leapfrogging vortex rings’, originally conjectured by Helmholtz in 1858.
This video was produced by the SITE Research Center at New York University, as part of their talk series.
