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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 (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
14
Publisher
Wiley
Pages
1665–1672
Publication identifier
http://dx.doi.org/10.1002/mana.200410331
Metadata
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Author(s)
Gallagher, Isabelle
Gallay, Thierry
Lions, Pierre-Louis
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

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