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Comptes Rendus Mathématique
Volume 340, n° 1
pages 31-36 (janvier 2005)
Doi : 10.1016/j.crma.2004.10.016
Received : 5 July 2004 ;  accepted : 15 October 2004
On the regularity up to the boundary in the theory of the Navier-Stokes equations with generalized impermeability conditions
Régularité conditionnelle jusquʼà la frontière du domaine en théorie des équations de Navier-Stokes associées à des conditions limites dʼimperméabilité généralisée
 

Jiří Neustupa a , Patrick Penel b
a Czech Technical University, Faculty of Mechanical Engineering, Department of Technical Mathematics, Karlovo nám. 13, 121 35 Praha 2, Czech Republic 
b Université du Sud, Toulon-Var, département de mathématique, BP 20132, 83957 La Garde, France 

Abstract

In this Note, we extend sufficient conditions for regularity we described in our previous works so that they are valid not only in the interior, but up to the boundary of a flow field. The conditions are based on the integrability properties of either one of the eigenvalues of the rate of deformation tensor or one component of velocity. To cite this article: J. Neustupa, P. Penel, C. R. Acad. Sci. Paris, Ser. I 340 (2005).

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

Dans cette Note, nous étendons jusquʼà la frontière du domaine spatial, les conditions suffisantes pour la régularité des solutions faibles des équations de Navier-Stokes que nous avions obtenues dans nos travaux précédents. Ces conditions sont basées sur les propriétés dʼintégrabilité ou bien dʼune des valeurs propres du tenseur de déformation, ou bien dʼune des composantes du champ de vitesse. Pour citer cet article : J. Neustupa, P. Penel, C. R. Acad. Sci. Paris, Ser. I 340 (2005).

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


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