Strong solutions in $L^2$ framework for fluid-rigid body interaction problem. Mixed case

Abstract

The paper deals with the problem describing the motion of a rigid body inside a viscous incompressible fluid when the mixed boundary conditions are considered. At the fluid-rigid body interface the slip Navier boundary condition is prescribed, having the continuity of velocity just in the normal component, and the Dirichlet condition is given on the boundary of the fluid domain. The existence and uniqueness of the local strong solution is proven by the local transformation and the fixed point argument.