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Comptes Rendus Mathématique
Volume 341, n° 6
pages 387-392 (septembre 2005)
Doi : 10.1016/j.crma.2005.07.023
Received : 23 Mars 2005 ;  accepted : 19 July 2005
Solutions faibles H2 pour un modèle de fluide non newtonien
Weak solutions   for a non-Newtonian fluid model
 

Cherif Amrouche a , El-Hacene Ouazar b
a Laboratoire de mathématiques appliquées, CNRS, UMR 51-42, université de Pau et des pays de lʼAdour, 64000 Pau, France 
b École normale supérieure de Kouba, département de mathématiques, Alger, Algérie 

Résumé

Lʼobjet de ce travail est dʼétudier un système non linéaire modélisant un écoulement de fluide non newtonien, solution aqueuse de polymères. On sʼintéresse ici à lʼexistence de solutions faibles pour le problème stationnaire dans un ouvert borné ou extérieur du plan. Une première difficulté tient au fait quʼon cherche celles-ci dans lʼespace naturel fourni par les équations dʼénergie, ce qui se complique encore lorsque le domaine est non borné. La seconde est due au fait que, dans les équations, le terme de viscosité est de dérivée dʼordre 2, alors que le terme non linéaire est dʼordre 3. Pour citer cet article : C. Amrouche, E.-H. Ouazar, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

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Abstract

This Note is devoted to the study a non-linear system modelling a flow of a non-Newtonian fluid, namely aqueous polymer solutions. In the present work, we prove a theorem on the existence of weak solutions for the steady-state problem in a bounded or exterior plane domain. A first difficulty is due to the fact that we search these solutions in the natural space given by the energy inequalities. The second difficulty stems from the fact that the non-linear term involves a third-order derivative, whereas its elliptic term is only a Laplace operator. To cite this article: C. Amrouche, E.-H. Ouazar, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

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