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We consider a fluid-structure interaction system composed by a rigid ballimmersed into a viscous incompressible fluid. The motion of the structuresatisfies the Newton laws and the fluid equations are the standardNavier-Stokes system. At the boundary of the fluid domain, we use the Trescaboundary conditions, that permit the fluid to slip tangentially on the boundaryunder some conditions on the stress tensor. More precisely, there is athreshold determining if the fluid can slip or not and there is a frictionforce acting on the part where the fluid can slip. Our main result is theexistence of contact in finite time between the ball and the exterior boundaryof the fluid for this system in the bidimensional case and in presence ofgravity.

Existence of contacts for the motion of a rigid body into a viscous incompressible fluid with the Tresca boundary conditions