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Uniqueness in linearized two-dimensional water-wave problems

Published online by Cambridge University Press:  20 April 2006

M. J. Simon  and
F. Ursell
M. J. Simon
Affiliation:
Department of Mathematics, University of Manchester
F. Ursell
Affiliation:
Department of Mathematics, University of Manchester
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Abstract

A geometrical condition sufficient for uniqueness in two-dimensional time-periodic linear water-wave problems is derived, and some examples are given. The technique can be seen as a generalization of work by John (1950), who established uniqueness for surface-piercing bodies that have the property that vertical lines down from the free surface do not intersect the body.

The paper is in two parts. Part 1 provides a review of current knowledge on the topic of uniqueness, and gives a simple form of John's proof. Part 2 describes the recent progress, in which the ideas of John's proof are extended so that uniqueness can be demonstrated for surface-piercing bodies that do not satisfy John's geometrical criterion. In fact the new technique proves uniqueness for a large class of problems involving floating bodies, submerged bodies and multiple-body systems. However, the present work still does not constitute a general proof of uniqueness for all configurations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 148 , November 1984 , pp. 137 - 154
Copyright
© 1984 Cambridge University Press

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