A note on uniqueness in the linearized water-wave problem

Citation
Ng. Kuznetsov et Mj. Simon, A note on uniqueness in the linearized water-wave problem, J FLUID MEC, 386, 1999, pp. 5-14
Citations number
20
Categorie Soggetti
Physics,"Mechanical Engineering
Journal title
JOURNAL OF FLUID MECHANICS
ISSN journal
00221120 → ACNP
Volume
386
Year of publication
1999
Pages
5 - 14
Database
ISI
SICI code
0022-1120(19990510)386:<5:ANOUIT>2.0.ZU;2-Y
Abstract
The uniqueness theorem of Simon & Ursell (1984), concerning the linearized two-dimensional water-wave problem in a fluid of infinite depth, is extende d in two directions. First, we consider a two-dimensional geometry involvin g two submerged symmetric bodies placed sufficiently far apart that they ar e not confined in the vertical right angle having its vertex on the free su rface as the theorem of Simon & Ursell requires. A condition is obtained gu aranteeing the uniqueness outside a finite number of bounded frequency inte rvals. Secondly, the method of Simon & Ursell is generalized to prove uniqu eness in the axisymmetric problem for bodies violating John's condition pro vided the free surface is a connected plane region.