Collisions in 3D Fluid Structure interactions problems

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

This paper deals with the system composed by a rigid ball moving into a viscous incompressible fluid, over a fixed horizontal plane. The equations of motion for the fluid are the Navier-Stokes equations and the equations for the motion of the rigid ball are obtained by applying Newton's laws. We show that for any weak solutions of the corresponding system satisfying the energy inequality, the rigid ball never touches the plane.

Domaines: Equations aux dérivées partielles [math.AP]

Matthieu Hillairet, Takéo Takahashi. Collisions in 3D Fluid Structure interactions problems. SIAM Journal on Mathematical Analysis, 2009, 40 (6), pp.2451-2477. ⟨10.1137/080716074⟩. ⟨hal-00268987⟩