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

We consider a fluid-structure interaction system composed by rigid ball immersed into viscous in-compressible fluid. The motion of the structure satisfies Newton laws and fluid equations are standard Navier-Stokes system. At boundary domain, we use Tresca conditions, that permit to slip tangentially on under some conditions stress tensor. More precisely, there is threshold determining if can or not friction force acting part where slip. Our main result existence contact in finite time between exterior for this bidimensional case presence gravity.