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Optimal Results For The Two Dimensional Navier-Stokes Equations With Lower Regularity On The Data

Fontes, Magnus LU and Eero, Saksman (2004) In Seminaires et Congres 9. p.143-154
Abstract
We establish existence and uniqueness of solutions in the anisotropic Sobolev space H^{1,1/2} to the two dimensional Navier-Stokes equations with source data in H^{-1,-1/2}. Our results give a new elementary proof for and extend some recent results by G. Grubb.
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Contribution to journal
publication status
published
subject
keywords
anisotropic Sobolev space, Navier Stokes, Hilbert transform, fractional calculus
in
Seminaires et Congres
volume
9
pages
143 - 154
publisher
Société Mathématiques de France
ISSN
1285-2783
language
English
LU publication?
yes
additional info
Résumé (Résultats optimaux pour les équations de Navier-Stokes en dimension 2 avec des données initiales peu régulières) On ´etablit l’existence et l’unicit´e des solutions dans l’espace de Sobolev anisotrope H1,1/2 pour les ´equations de Navier-Stokes en dimension 2 avec des donn´ees dans H−1,−1/2. Nos r´esultats donnent une preuve ´el´ementaire nouvelle de r´esultats r´ecents de G. Grubb, tout en les compl´etant.
id
28b0601b-3335-4060-be6c-790f114ab97d (old id 933613)
alternative location
http://www.emis.de/journals/SC/2004/9/pdf/smf_sem-cong_9_143-154.pdf
date added to LUP
2016-04-01 16:31:21
date last changed
2018-11-21 20:42:04
@article{28b0601b-3335-4060-be6c-790f114ab97d,
  abstract     = {{We establish existence and uniqueness of solutions in the anisotropic Sobolev space H^{1,1/2} to the two dimensional Navier-Stokes equations with source data in H^{-1,-1/2}. Our results give a new elementary proof for and extend some recent results by G. Grubb.}},
  author       = {{Fontes, Magnus and Eero, Saksman}},
  issn         = {{1285-2783}},
  keywords     = {{anisotropic Sobolev space; Navier Stokes; Hilbert transform; fractional calculus}},
  language     = {{eng}},
  pages        = {{143--154}},
  publisher    = {{Société Mathématiques de France}},
  series       = {{Seminaires et Congres}},
  title        = {{Optimal Results For The Two Dimensional Navier-Stokes Equations With Lower Regularity On The Data}},
  url          = {{http://www.emis.de/journals/SC/2004/9/pdf/smf_sem-cong_9_143-154.pdf}},
  volume       = {{9}},
  year         = {{2004}},
}