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Comptes Rendus Mathématique
Volume 343, n° 1
pages 31-36 (juillet 2006)
Doi : 10.1016/j.crma.2006.04.024
Received : 5 December 2005 ;  accepted : 21 April 2006
Régularité conditionnelle des équations de Navier-Stokes
Conditional regularity of the 3D Navier-Stokes equation
 

Igor Kukavica , Mohammed Ziane
Department of Mathematics, University of Southern California, Los Angeles, California, États-Unis 

Résumé

Dans cette Note, nous donnons des conditions suffisantes de régularité des solutions des équations de Navier-Stokes. Nous montrons que si une solution de Leray-Hopf vérifie lʼune des trois conditions (i)   où   et  , (ii)   où   et  , ou (iii)   où   et  , alors elle est régulière. Ces conditions améliorent les résultats existants sur la régularité conditionnelle des équations de Navier-Stokes. Pour citer cet article : I. Kukavica, M. Ziane, C. R. Acad. Sci. Paris, Ser. I 343 (2006).

The full text of this article is available in PDF format.
Abstract

In this Note, we give sufficient conditions for the regularity of Leray-Hopf weak solutions to the Navier-Stokes equation. We prove that, if one of three conditions (i)   where   and  , (ii)   where   and  , or (iii)   where   and  , is satisfied, then the solution is regular. These conditions improve earlier results on the conditional regularity of the Navier-Stokes equations. To cite this article: I. Kukavica, M. Ziane, C. R. Acad. Sci. Paris, Ser. I 343 (2006).

The full text of this article is available in PDF format.


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