Existence of weak solutions for an interaction problem between an elastic structure and a compressible viscous fluid

Muriel Boulakia

doi:10.1016/j.crma.2004.11.003

Partial Differential Equations/Mathematical Problems in Mechanics

Existence of weak solutions for an interaction problem between an elastic structure and a compressible viscous fluid

Presented by: Pierre-Louis Lions

Muriel Boulakia ¹

¹ Laboratoire de mathématiques appliquées, université de Versailles-St-Quentin, 45, avenue des Etats Unis, 78035 Versailles cedex, France

Comptes Rendus. Mathématique, Volume 340 (2005) no. 2, pp. 113-118.

Abstract
Résumé

We prove an existence result of weak solutions for an interaction problem between an elastic structure and a compressible fluid in three space dimensions. Solutions are defined as long as there is no collision and as long as conditions of non-interpenetration and of preservation of orientation are satisfied by the displacement field of the structure.

Nous présentons ici un résultat d'existence de solutions faibles pour un problème d'interaction entre une structure élastique et un fluide compressible en dimension trois. Les solutions sont définies tant qu'il n'y pas de chocs et tant que le déplacement de la structure vérifie des conditions de non-interpénétration et de préservation de l'orientation.

Received: 2004-07-18
Accepted: 2004-10-29
Published online: 2004-12-24

DOI: 10.1016/j.crma.2004.11.003

Author's affiliations:

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 an interaction problem between an elastic structure and a compressible viscous fluid. Comptes Rendus. Mathématique, Volume 340 (2005) no. 2, pp. 113-118. doi : 10.1016/j.crma.2004.11.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.11.003/

References
Cited by

[1] M. Boulakia, Modélisation et analyse mathématique de problèmes d'interaction fluide–structure, Thesis, université de Versailles, 2004

[2] B. Desjardins; M.J. Esteban On weak solutions for fluid-rigid structure interaction: compressible and incompressible models, Commun. Partial Differential Equations, Volume 25 (2000) no. 7–8, pp. 1399-1413

[3] R.J. Di Perna; P.-L. Lions Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math., Volume 98 (1989), pp. 511-547

[4] E. Feireisl On the motion of rigid bodies in a viscous compressible fluid, Arch. Rational Mech. Anal., Volume 167 (2003) no. 4, pp. 281-308

[5] E. Feireisl; A. Novotny`; H. Petzeltovà On the existence of globally defined weak solutions to the Navier–Stokes equations, J. Math. Fluid Mech., Volume 3 (2001) no. 4, pp. 358-392

[6] F. Flori; P. Orenga Fluid–structure interaction: analysis of a 3-D compressible model, Ann. Inst. H. Poincaré Anal. Non Linéaire, Volume 17 (2000) no. 6, pp. 753-777

[7] P.L. Lions Mathematical Topics in Fluid Mechanics, Oxford Science Publications, 1996

[8] P.L. Lions Bornes sur la densité pour les équations de Navier–Stokes compressibles isentropiques avec conditions aux limites de Dirichlet, C. R. Acad. Sci. Paris, Ser. I, Volume 328 (1999) no. 8, pp. 659-662

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