On the uniqueness of the solution of the two-dimensional Navier-Stokes   equation with a Dirac mass as initial vorticity
  We propose two different proofs of the fact that Oseen's vortex is the unique solution of the two-dimensional Navier-Stokes equation with a Dirac mass as initial vorticity. The first argument, due to C.E. Wayne and the second author, is based on an entropy estimate for the vorticity equation in self-similar variables. The second proof is new and relies on symmetrization techniques for parabolic equations. 
Isabelle Gallagher, Thierry Gallay, Pierre-Louis Lions