On the dynamics of vortices in viscous 2D flows

Abstract

We study the 2D Navier--Stokes solution starting from an initial vorticity mildly concentrated near $N$ distinct points in the plane. We prove quantitative estimates on the propagation of concentration near a system of interacting point vortices introduced by Helmholtz and Kirchhoff. Our work extends the previous results in the literature in three ways: The initial vorticity is concentrated in a weak (Wasserstein) sense, it is merely $L^p$ integrable for some $p>2$, and the estimates we derive are uniform with respect to the viscosity.