Th. Gallay, C.E. Wayne
Global stability of vortex solutions of the two-dimensional
Navier-Stokes equation
(507K, Postscript)
ABSTRACT. 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.