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

Gallagher, Isabelle; Gallay, Thierry; Lions, Pierre-Louis

Gallagher, Isabelle; Gallay, Thierry; Lions, Pierre-Louis (2005), On the uniqueness of the solution of the two-dimensional Navier–Stokes equation with a Dirac mass as initial vorticity, Mathematische Nachrichten, 278, 14, p. 1665–1672. http://dx.doi.org/10.1002/mana.200410331

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Type

Article accepté pour publication ou publié

Date

2005

Journal name

Mathematische Nachrichten

Volume

278

Number

Publisher

Wiley

Pages

1665–1672

Abstract (EN)

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 named 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.

Subjects / Keywords

Navier–Stokes equations; vorticity; uniqueness; self-similar variables; entropy estimates; symmetric nonincreasing rearrangements