Collisions in Three-Dimensional Fluid Structure Interaction Problems

This paper deals with a system composed of 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 solution of the corresponding system satisfying the energy inequality, the rigid ball never touches the plane. This result is the extension of that obtained in [M. Hillairet, Comm. Partial Differential Equations, 32 (2007), pp. 1345–1371] in the two-dimensional setting.