A uniqueness criterion for linear problems of wave-body interaction

The question of uniqueness for linearized problems describing interaction of submerged bodies with an ideal unbounded fluid is far from its final resolution. In the present work a new criterion of uniqueness is suggested based on Green’s integral identity and maximum principles for elliptic differential equations. The criterion is formulated as an inequality involving integrals of the Green function over the bodies’ wetted contours. This criterion is quite general and applicable for any number of submerged bodies of fairly arbitrary shape (satisfying an exterior sphere condition) and in any dimension; it can also be generalised to more complicated elliptic problems. Very simple bounds are also derived from the criterion, which deliver uniqueness sets in the space of parameters defined by submergence of the system of bodies and the frequency of oscillation. Results of numerical investigation and comparison with known uniqueness criteria are presented. Introduction This article is concerned with the two and three-dimensional linear boundaryvalue problems of the interaction between an ideal unbounded fluid and bodies located under the free surface of the fluid. Two classes of problem, describing the radiation of waves by the forced motion of rigid bodies and the diffraction of waves by fixed rigid bodies, appear within the framework of the surface wave theory under the usual assumptions that the motion is steady-state, irrotational and the oscillations have small amplitudes. Our interest here is in the question of uniqueness. For these seemingly simple problems very few criteria of uniqueness are known despite the long history of