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

Isabelle Gallagher·Thierry Gallay·Pierre-Louis Lions
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Abstract

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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Isabelle Gallagher, Thierry Gallay, Pierre-Louis Lions. 2004-10-15. On the uniqueness of the solution of the two-dimensional Navier-Stokes equation with a Dirac mass as initial vorticity. https://arxiv.org/abs/math/0410344

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