Formation of small scales in nonlinear PDEs

Axi-symmetrization near point vortex solutions for the 2D Euler equation

Alex Ionescu

Princeton University

I will discuss a recent theorem on the asymptotic stability of point vortex solutions to the full Euler equation in 2 dimensions. More precisely, we show that a small, Gevrey smooth, and compactly supported perturbation of a point vortex leads to a global solution of the Euler equation in 2D, which converges weakly as the time goes to infinity to a radial profile with respect to a new vortex. The mechanism that leads to stabilization is mixing and inviscid damping. This is joint work with Hao Jia.