MATHEMATICAL STUDY OF THE SMALL OSCILLATIONS OF A FLOATING BODY IN A BOUNDED TANK CONTAINING AN INCOMPRESSIBLE VISCOUS LIQUID

The authors study the small oscillations of a floating body in a bounded tank containing an incompressible viscous fluid. Using the variational formulation of the problem, they obtain an operator equation from which they can study the spectrum of the problem. The small motions are strongly and weakly damped aperiodic motions and, if the viscosity is sufficiently small, there is also at most finite number of damped oscillatory motions. The authors give also an existence and uniqueness theorem for the solution of the associated evolution problem.