arXiv:math/0410344 Abstract

arXiv:math/0410344 [math.AP]Abstract References Reviews Resources

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

Published 2004-10-15Version 1

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.

Comments: 9 pages, no figure

Categories: math.AP, math-ph, math.MP

Subjects: 35Q30, 35A07, 76D05, 76D17

Keywords: two-dimensional navier-stokes equation, dirac mass, initial vorticity, uniqueness, symmetrization techniques

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