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

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Date
2005
Dewey
Analyse
Sujet
Navier–Stokes equations; vorticity; uniqueness; self-similar variables; entropy estimates; symmetric nonincreasing rearrangements
Journal issue
Mathematische Nachrichten
Volume
278
Number
14
Publication date
2005
Article pages
1665–1672
Publisher
Wiley
DOI
http://dx.doi.org/10.1002/mana.200410331
URI
https://basepub.dauphine.fr/handle/123456789/6169
Collections
  • CEREMADE : Publications
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Author
Gallagher, Isabelle
Gallay, Thierry
Lions, Pierre-Louis
Type
Article accepté pour publication ou publié
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.

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