A uniqueness criterion for linear problems of wave-body interaction

The question of uniqueness for problems describing the interaction of submerged bodies with an ideal unbound fluid is far from resolution. In the present work a new criterion of uniqueness is suggested based on Green's integral identity and the maximum principle for elliptic differential equations. The criterion is formulated as an inequality involving integrals of the Green's function over bodies' wetted contours, and when being satisfied guarantees uniqueness of the problem. This criterion is quite general and applicable for any number of bodies of arbitrary shape (satisfying the exterior sphere condition) and in any dimension.