Existence of weak solutions up to collision for viscous fluid-solid systems with slip
Hillairet, Matthieu; Gérard-Varet, David (2014), Existence of weak solutions up to collision for viscous fluid-solid systems with slip, Communications on Pure and Applied Mathematics, 67, 12, p. 2022-2076. http://dx.doi.org/10.1002/cpa.21523
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00713331
Journal nameCommunications on Pure and Applied Mathematics
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Abstract (EN)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.
Subjects / KeywordsCauchy theory; Navier Wall law; Navier Stokes equations; Fluid-solid interactions
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