Blow up and grazing collision in viscous fluid solid interaction systems

Matthieu Hillairet (1) , Takéo Takahashi (2, 3)

1 MIP - Mathématiques pour l'Industrie et la Physique
2 IECN - Institut Élie Cartan de Nancy
3 CORIDA - Robust control of infinite dimensional systems and applications

In this paper we investigate finite time blow up of strong solutions to the system describing the motion of a rigid ball inside a bounded cavity filled with a viscous incompressible fluid. The equations of motion for the fluid are of Navier--Stokes type and the equations for the motion of the rigid ball are obtained by applying Newton's laws. The whole system evolves under the action of gravity. First, we prove contact between the ball and the boundary of the cavity implies the blow up of the strong solution. Then we prove for some configurations such a contact has to occur in finite time.

Domaines: Equations aux dérivées partielles [math.AP]

Matthieu Hillairet, Takéo Takahashi. Blow up and grazing collision in viscous fluid solid interaction systems. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2010, 27 (1), pp.291-313. ⟨10.1016/j.anihpc.2009.09.007⟩. ⟨hal-00355684⟩