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A note on uniqueness in the linearized water-wave problem

Published online by Cambridge University Press:  10 May 1999

N. G. KUZNETSOV  and
M. J. SIMON
N. G. KUZNETSOV
Affiliation:
Laboratory for Mathematical Modelling of Wave Phenomena, Institute of Problems in Mechanical Engineering, Russian Academy of Sciences, V.O., Bol'shoy pr. 61, St Petersburg 199178, RF
M. J. SIMON
Affiliation:
Department of Mathematics, University of Manchester, Manchester, M13 9PL, UK
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Abstract

The uniqueness theorem of Simon & Ursell (1984), concerning the linearized two-dimensional water-wave problem in a fluid of infinite depth, is extended in two directions. First, we consider a two-dimensional geometry involving two submerged symmetric bodies placed sufficiently far apart that they are not confined in the vertical right angle having its vertex on the free surface as the theorem of Simon & Ursell requires. A condition is obtained guaranteeing the uniqueness outside a finite number of bounded frequency intervals. Secondly, the method of Simon & Ursell is generalized to prove uniqueness in the axisymmetric problem for bodies violating John's condition provided the free surface is a connected plane region.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 386 , 10 May 1999 , pp. 5 - 14
Copyright
© 1999 Cambridge University Press

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