The Rigid Body Motion in Cosserat's Fluid with Navier's Slip Boundary Conditions

The aim of the talk is to give a brief presentation of novel results related to the body-fluid interaction problem.
The motion is described by a system of coupled differential equations: Newton’s second law and Navier-Stokes type equations. We shall discuss the global solvability result of weak solution of the problem, when the slippage is allowed at the boundaries of the rigid body and of the bounded domain, occupied by the fluid.
This result completely resolves a famous non-contact paradox between the rigid body and the domain boundary.