  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.
