On the regularity of weak solutions to the fluid-rigid body interaction problem

We study a 3D fluid-rigid body interaction problem. The fluid flow is governed by 3D incompressible Navier-Stokes equations, while the motion of the rigid body is described by a system of ordinary differential equations describing conservation of linear and angular momentum. Our aim is to prove that any weak solution satisfying certain regularity conditions is smooth. This is a generalization of the classical result for the 3D incompressible Navier-Stokes equations, which says that a weak solution that additionally satisfy Prodi-Serrin L-r - L-s condition is smooth. We show that in the case of fluid-rigid body the Prodi-Serrin conditions imply W-2,W-p and W-1,W-p regularity for the fluid velocity and fluid pressure, respectively. Moreover, we show that solutions are C-infinity if additionally we assume that the rigid body acceleration is bounded almost anywhere in time variable.