Comptes Rendus
Partial Differential Equations/Mathematical Problems in Mechanics
Existence of weak solutions for the motion of an elastic structure in an incompressible viscous fluid
[Existence d'une solution faible pour un problème d'interaction fluide visqueux incompressible-solide élastique]
Comptes Rendus. Mathématique, Volume 336 (2003) no. 12, pp. 985-990.

We study here the two dimensional motion of an elastic body immersed in an incompressible viscous fluid. The body and the fluid are contained in a fixed bounded set Ω. We show the existence of a weak solution for regularized elastic deformations as long as elastic deformations are not too important and no collisions occur. A complete proof is given by Boulakia in existence d'une solution faible pour un problème d'interaction fluide visqueux incompressible-solide élastique (prepublication 104, UVSQ, 2003).

Nous étudions ici le mouvement d'un solide élastique immergé dans un fluide visqueux incompressible en dimension 2. L'ensemble fluide-structure évolue dans une cavité fixe bornée Ω. Nous montrons un résultat d'existence de solution faible de notre problème pour des déformations élastiques régularisées sous réserve qu'il n'y ait pas de chocs et que le solide n'ait pas de trop grosses déformations élastiques. Une preuve complète est donnée par Boulakia dans existence d'une solution faible pour un problème d'interaction fluide visqueux incompressible-solide élastique (prépublication 104, UVSQ, 2003).

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(03)00235-8

Muriel Boulakia 1

1 Laboratoire de mathématiques appliquées, Université de Versailles-St-Quentin, 45, avenue des Etats Unis, 78035 Versailles cedex, France
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Muriel Boulakia. Existence of weak solutions for the motion of an elastic structure in an incompressible viscous fluid. Comptes Rendus. Mathématique, Volume 336 (2003) no. 12, pp. 985-990. doi : 10.1016/S1631-073X(03)00235-8. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00235-8/

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