Long-time asymptotics for two-dimensional exterior flows with small   circulation at infinity
  We consider the incompressible Navier-Stokes equations in a two-dimensional exterior domain, with no-slip boundary conditions. We assume that the initial velocity is a finite-energy and L^q-summable perturbation of the Oseen vortex with circulation \alpha, where 1 < q < 2. If {\alpha} is sufficiently small, we show that the solution behaves asymptotically in time like the self-similar Oseen vortex with circulation \alpha. This is a global stability result, which holds for arbitrarily large perturbations of the Oseen vortex, and our smallness assumption on the circulation is independent of the domain under consideration. 
Thierry Gallay and Yasunori Maekawa
math.AP