Comptes Rendus
Partial Differential Equations/Mathematical Problems in Mechanics
Weak convergence results for inhomogeneous rotating fluid equations
Comptes Rendus. Mathématique, Volume 336 (2003) no. 5, pp. 401-406.

We consider the equations governing incompressible, viscous fluids in three space dimensions, rotating around an inhomogeneous vector B(x): this is a generalization of the usual rotating fluid model (where B is constant). We prove the weak convergence of Leray-type solutions towards a vector field which satisfies the usual 2D Navier–Stokes equation in the regions of space where B is constant, with Dirichlet boundary conditions, and a heat–type equation elsewhere. The method of proof uses weak compactness arguments.

On considère les équations modélisant des fluides incompressibles et visqueux en trois dimensions d'espace, en rotation rapide autour d'un vecteur non homogène B(x) : on généralise ainsi le modèle habituel des fluides tournants (où B est constant). On montre la convergence des solutions de Leray vers un champ de vecteurs qui vérifie les équations habituelles de Navier–Stokes 2D dans les régions de l'espace où B est constant, avec des conditions aux limites de Dirichlet, et une équation de type chaleur ailleurs. La méthode de démonstration repose sur des arguments de compacité faible.

Received:
Accepted:
Published online:
DOI: 10.1016/S1631-073X(03)00066-9

Isabelle Gallagher 1; Laure Saint-Raymond 2

1 Centre de mathématiques, UMR 7640, École polytechnique, 91128 Palaiseau, France
2 Laboratoire Jacques-Louis Lions, UMR 7598, boı̂te 187, Université Paris-VI, 4, place Jussieu, 75252 Paris cedex 05, France
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Isabelle Gallagher; Laure Saint-Raymond. Weak convergence results for inhomogeneous rotating fluid equations. Comptes Rendus. Mathématique, Volume 336 (2003) no. 5, pp. 401-406. doi : 10.1016/S1631-073X(03)00066-9. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00066-9/

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