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On the uniqueness of the solution of the two‐dimensional Navier–Stokes equation with a Dirac mass as initial vorticity
Author(s) -
Gallagher Isabelle,
Gallay Thierry,
Lions PierreLouis
Publication year - 2005
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200410331
Subject(s) - symmetrization , mathematics , vorticity , uniqueness , vorticity equation , mathematical proof , mathematical analysis , vortex , burgers vortex , mathematical physics , physics , geometry , thermodynamics
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. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)