Global stability of vortex solutions of the two-dimensional Navier-Stokes equation

Both experimental and numerical studies of fluid motion indicate that initially localized regions of vorticity tend to evolve into isolated vortices and that these vortices then serve as organizing centers for the flow. In this paper we prove that in two dimensions localized regions of vorticity do evolve toward a vortex. More precisely we prove that any solution of the two-dimensional Navier-Stokes equation whose initial vorticity distribution is integrable converges to an Oseen vortex, an explicit solution of the two-dimensional Navier-Stokes equation. Under slightly stronger hypotheses we also give precise estimates on the rate of convergence toward the vortex.