On the dynamics of vortices in viscous 2D flows

Abstract

AbstractWe 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 $$L^p$$ L p integrable for some $$p>2$$ p > 2 , and the estimates we derive are uniform with respect to the viscosity.