Equilibrium Configurations and their Uniqueness in a Fluid-Solid Interaction Problem

We demonstrate existence in the large" and uniqueness in the small" of equilibrium configurations for the coupled system consisting of a Navier-Stokes fluid interacting with a rigid body subjected to spring forces and restoring moments. The driving mechanism is a uniform, given velocity field of the fluid at large spatial distances from the body. The main difficulty in the proof of the above properties arises from the fact that the body can rotate around a given axis, which produces a highly nonlinear problem.