Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On the solvability of a two-dimensional wave-body interaction problem

Authors: G. A. Athanassoulis and C. G. Politis
Journal: Quart. Appl. Math. 48 (1990), 1-30
MSC: Primary 35Q35; Secondary 31A35, 76B15
DOI: https://doi.org/10.1090/qam/1040231
MathSciNet review: MR1040231
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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 $ {L^P}\left( { - \pi , 0} \right)$, $ 1 < p \le 2$. Strict estimates of the form $ {D_n} = O\left( {n^{ - \alpha }} \right)$ are also obtained for the coefficients of the multipole-series expansion for piecewise smooth $ \left( {0 < \alpha < 2} \right)$ and smooth $ \left( {\alpha = 2} \right)$ body boundaries.

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DOI: https://doi.org/10.1090/qam/1040231
Article copyright: © Copyright 1990 American Mathematical Society

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