Analysis and Probability Seminar

A long-standing topic of interest is to understand solutions of the incompressible 2D Euler equations that approximate point vortices in the sense that the vorticity of the solution stays highly concentrated around a finite number of points on some interval of time. There are a large class of steady states that satisfy this behaviour, and also solutions that exhibit this behaviour dynamically on finite time intervals. We exhibit solutions of 2D Euler that are genuinely dynamic, and also retain this concentration of vorticity around points for all time: a configuration approximating two vortex pairs separating at linear speed, and a configuration approximating three vortices separating like a self-similar spiral at sublinear speed. Joint work with Juan Davila, Manuel Del Pino, and Monica Musso.