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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Article accepté pour publication ou publiéDate
2005Journal name
Mathematische NachrichtenVolume
278Number
14Publisher
Wiley
Pages
1665–1672
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Show full item recordAbstract (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 rearrangementsRelated items
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