Title :

On the global well-posedness of the 2D Euler equations for a large class of Yudovich type data

Author(s) :

Bernicot, Frederic [Auteur correspondant]
Laboratoire de Mathématiques Jean Leray [LMJL]
Keraani, Sahbi [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Annales Scientifiques de l'École Normale Supérieure

Pages :

559-576

Publisher :

Société mathématique de France

Publication date :

2014

ISSN :

0012-9593

Keyword(s) :

2D incompressible Euler equations
Global well-posedness
BMO-type space

HAL domain(s) :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]

English abstract : [en]

The study of the 2D Euler equation with non Lipschitzian velocity was initiated by Yudovich in [19] where a result of global well-posedness for essentially bounded vorticity is proved. A lot of works have been since dedicated ...
Show more >The study of the 2D Euler equation with non Lipschitzian velocity was initiated by Yudovich in [19] where a result of global well-posedness for essentially bounded vorticity is proved. A lot of works have been since dedicated to the extension of this result to more general spaces. To the best of our knowledge all these contributions lack the proof of at least one of the following three fundamental properties: global existence, uniqueness and regularity persistence. In this paper we introduce a Banach space containing unbounded functions for which all these properties are shown to be satisfied.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Analyse de Fourier Multilineaire et EDPs Nonlineaires
Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation

Comment :

17 pages

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL