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Abstract

Abstract. The two-dimensional, deep-water, wave-body interaction problem for a single-hulled body, floating on the free surface of an ideal liquid, is considered. The body boundary may be nonsmooth and may intersect the free surface at arbitrary angles. The existence of a unique solution representable by a multipole-series expansion is proved for all but a discrete set of oscillation frequencies. The proof is based on the property of the associated multipoles to be a basis of the space Lp(-n,0), 1 < p < 2. Strict estimates of the form Dn -0(n~a) are also obtained for the coefficients of the multipole-series expansion for piecewise smooth (0 < a < 2) and smooth (a = 2) body boundaries.1. Introduction. Consider an infinitely long, horizontal cylinder floating on the free surface of an unbounded, infinitely deep, incompressible and inviscid liquid. In this paper we are concerned with the solvability (well-posedness) of the boundary-value problems arising when the floating body is forced, by an incident harmonic wave or by an external force, to perform time-harmonic oscillations of small amplitude about its position of stable hydrostatic equilibrium.The uniqueness question for the wave-floating body interaction problem has been studied by means of two, essentially different, methodologies. The first one is of geometric character and appropriately uses Green's theorem to ensure that the only possible solution of the homogeneous problem is the trivial one. Such an approach was inaugurated by John [18] in 1950 (see also Lenoir [24], who reworked the twodimensional case, and Kleinman [21]). Recently, Simon and Ursell [33] essentially generalized John's uniqueness theorem in a manner permitting them to consider floating and/or submerged bodies of quite a general shape. In general, the uniqueness results obtained via this methodology are valid for all wavelengths but have suffered, up to now, from some geometrical restrictions concerning the shape of the floating body. Having established uniqueness, the well-posedness of the problem can be deduced by using various methods, such as the integral-equation formulation [18,21,22] or the limiting absorption principle [11,24,25].