Some Remarks on the Boundary Conditions  in the Theory of Navier-Stokes Equations

Chérif Amrouche; Patrick Penel; Nour Seloula

doi:10.5802/ambp.321

Some Remarks on the Boundary Conditions in the Theory of Navier-Stokes Equations
[Théorie des Équations de Navier-Stokes : Remarques sur les Conditions aux Limites]

Chérif Amrouche ¹ ; Patrick Penel ² ; Nour Seloula ³

¹ Université de Pau et des Pays de l’Adour LMA, Avenue de l’Université 64013 Pau cedex, France
² Université du Sud, Toulon - Var 83957 La Garde cedex , France
³ Laboratoire de Mathématiques Nicolas Oresme UMR 6139 CNRS BP 5186 Université de Caen Basse Normandie

Annales mathématiques Blaise Pascal, Tome 20 (2013) no. 1, pp. 37-73.

Résumé
Abstract

Cet article traite de quelques questions théoriques relatives au choix des conditions aux limites, essentielles pour la modélisation et la simulation numérique en mécanique des fluides mathématique. Nous marquons la différence avec le choix standard de conditions de non glissement en soulignant trois ensembles de conditions autorisant glissement, et en insistant particulièrement sur l’interaction entre cadre fonctionnel approprié et statut de ces conditions.

This article addresses some theoretical questions related to the choice of boundary conditions, which are essential for modelling and numerical computing in mathematical fluids mechanics. Unlike the standard choice of the well known non slip boundary conditions, we emphasize three selected sets of slip conditions, and particularly stress on the interaction between the appropriate functional setting and the status of these conditions.

MR Zbl

DOI : 10.5802/ambp.321

Classification : 35Q35, 35A01, 76D05
Mots clés : Navier-Stokes, Boundary conditions, Weak solutions

Affiliations des auteurs :

Chérif Amrouche ¹ ; Patrick Penel ² ; Nour Seloula ³

¹ Université de Pau et des Pays de l’Adour LMA, Avenue de l’Université 64013 Pau cedex, France
² Université du Sud, Toulon - Var 83957 La Garde cedex , France
³ Laboratoire de Mathématiques Nicolas Oresme UMR 6139 CNRS BP 5186 Université de Caen Basse Normandie

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     journal = {Annales math\'ematiques Blaise Pascal},
     pages = {37--73},
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Chérif Amrouche; Patrick Penel; Nour Seloula. Some Remarks on the Boundary Conditions  in the Theory of Navier-Stokes Equations. Annales mathématiques Blaise Pascal, Tome 20 (2013) no. 1, pp. 37-73. doi : 10.5802/ambp.321. https://ambp.centre-mersenne.org/articles/10.5802/ambp.321/

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