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hal-00713331, version 1

Existence of weak solutions up to collision for viscous fluid-solid systems with slip

David Gérard-Varet () 1, Matthieu Hillairet () 2

(29/06/2012)

Résumé : We study in this paper the movement of a rigid solid inside an incompressible Navier-Stokes flow, within a bounded domain. We consider the case where slip is allowed at the fluid/solid interface, through a Navier condition. Taking into account slip at the interface is very natural within this model, as classical no-slip conditions lead to unrealistic collisional behavior between the solid and the domain boundary. We prove for this model existence of weak solutions of Leray type, up to collision, in three dimensions. The key point is that, due to the slip condition, the velocity field is discontinuous across the fluid/solid interface. This prevents from obtaining global H1 bounds on the velocity, which makes many aspects of the theory of weak solutions for Dirichlet conditions unadapted.

  • 1 :  Institut de Mathématiques de Jussieu (IMJ)
  • CNRS : UMR7586 – Université Pierre et Marie Curie (UPMC) - Paris VI – Université Paris VII - Paris Diderot
  • 2 :  CEntre de REcherches en MAthématiques de la DEcision (CEREMADE)
  • CNRS : UMR7534 – Université Paris IX - Paris Dauphine
  • Domaine : Mathématiques/Equations aux dérivées partielles
  • Mots-clés : Fluid-solid interactions – Navier Stokes equations – Navier Wall law – Cauchy theory
  • Commentaire : 45 pages
 
  • hal-00713331, version 1
  • http://hal.archives-ouvertes.fr/hal-00713331
  • oai:hal.archives-ouvertes.fr:hal-00713331
  • Contributeur : Matthieu Hillairet <>
  • Soumis le : Lundi 2 Juillet 2012, 12:14:35
  • Dernière modification le : Lundi 2 Juillet 2012, 20:53:03