On the motion of a liquid-filled rigid body subject to a time-periodic torque

Abstract

In this paper we investigate the existence of time-periodic motions of a system constituted by a rigid body with an interior cavity completely filled with a viscous liquid, and subject to a time-periodic external torque acting on the rigid body. We then show that the system of equations governing the motion of the coupled system liquid-filled rigid body, has at least one corresponding time-periodic weak solution. Furthermore if the size of the torque is below a certain constant, the weak solution is in fact strong.