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 this 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 surfaces. This criterion is quite general and applicable for any number of submerged bodies of arbitrary shape (provided the boundary is sufficiently regular) and in any dimension; it can also be generalized 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.