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Comptes Rendus Mathématique
Volume 334, n° 7
pages 609-613 (2002)
Doi : S1631-073X(02)02313-0
Received : 4 February 2002 ; 
Solutions variationnelles du problème stationnaire des fluides de grade trois
Variational solutions of stationary problem of third grade fluids
 

Jean-Marie Bernard a, El Hacène Ouazar b
a IUT d'Evry Val d'Essonne, 22, allée Jean-Rostand, 91025 Evry cedex, France 
b École normale supérieure, Kouba, 16050 Alger, BP 92, Algérie 

Note présentée par Philippe G. Ciarlet

Résumé

Dans cette Note, consacrée au problème stationnaire des fluides de grade trois, nous montrons l'existence de solutions et l'unicité, pour une frontière de classe C2,1 et une donnée petite, par une méthode d'estimations d'énergie. La résolution de ce problème en dimension trois requière une condition sur les paramètres intervenant dans l'équation, qui permet de montrer que l'opérateur différentiel de l'équation vérifie des propriétés d'ellipticité. Pour citer cet article : J.-M. Bernard, E.H. Ouazar, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 609-613.

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

We show the existence of solutions and the uniqueness of the stationary problem of third grade fluids, for a boundary of class C2,1 and small data, by a method of energy estimates. The resolution of the problem of third grade fluids in three dimensions requires a condition on the parameters occuring in the equation, which allows us to show that the differential operator of the equation verifies properties of ellipticity. To cite this article: J.-M. Bernard, E.H. Ouazar, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 609-613.

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


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