The problem of seakeeping

We consider the unsteady motion of a rigid body floating in a basin under the action of gravity, of the water pressure and of other prescribed extenrnal forces. The system is assumed to be initially in a rest position of equilibrium and the linear model is adopted. We prove an existence -uniqueness theorem via a suitable decomposition of the governing evolution equations of the system. The solution enjoies regularity with respect to time if the forcing term is switched on mildlyenough at the initial time, or if it starts with a finite jump, provided the body-inertia coefficients are sufficiently large.