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
TypeArticle accepté pour publication ou publié
Journal nameMathematische Nachrichten
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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 / KeywordsNavier–Stokes equations; vorticity; uniqueness; self-similar variables; entropy estimates; symmetric nonincreasing rearrangements
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