On the Motion of a Rigid Body in a Navier-Stokes Liquid Under the Action of a Time-Periodic Force

Indiana University Mathematics Journal, 58(6) (2009), 2805-2842
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This paper is devoted to the motion of a rigid body in an infinite Navier-Stokes liquid under the action of a time-periodic external force. Assuming that, with respect to an inertial reference frame, the force acts along a fixed direction, we investigate the existence of weak and strong periodic solutions to the equations of the coupled system body-liquid.