On the uniqueness of the solution of the two-dimensional Navier-Stokes equation with a Dirac mass as initial vorticity

Details On the uniqueness of the solution of the two-dimensional Navier-Stokes equation with a Dirac mass as initial vorticity On the uniqueness of the solution of the two-dimensional Navier-Stokes equation with a Dirac mass as initial vorticity

2004-10-15

arxiv.org/abs/math/0410344v1

Mathematics

Analysis of PDEs

9 pages, no figure

Scientific paper

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.

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