Comptes Rendus
no. 1
Uniqueness in the water-wave problem for bodies intersecting the free surface at arbitrary angles
[L'unicité du problème des ondes de surface pour les corps qui intersectent la surface libre sous des angles arbitraires]

Présenté par : Évariste Sanchez-Palencia

Nikolay Kuznetsov1
1 Laboratory for Mathematical Modelling of Wave Phenomena, Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, V.O., Bol'shoy pr. 61, St. Petersburg 199178, Russian Federation
Comptes Rendus. Mécanique, Volume 332 (2004) no. 1, pp. 73-78.

Cette Note porte sur un problème linéarisée du mouvement sur la houle d'un cylindre flottant dans une mer de profondeur infinie. L'unicité du problème est démontrée pour toutes les valeurs de la fréquence d'ondes si la forme du cylindre qui peut intersecter la surface libre sous d'angles arbitraires satisfait á des certaines conditions géométriques.

This Note deals with the linearized water-wave problem involving a surface-piercing cylinder in water of infinite depth. A solution to this problem is proved to be unique for all values of the radian frequency when the cylinder intersecting the free surface at arbitrary angles is subjected to certain geometric arrangements.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2003.10.008
Keywords: Fluid mechanics, Water waves, Floating cylinder, Conformal mapping, Integral identity, Uniqueness theorem
Mot clés : Mécanique des fluides, Ondes de surface, Cylindre flottant, Transformation conforme, Identité intégrale, Théorème d'unicité
Nikolay Kuznetsov 1

1 Laboratory for Mathematical Modelling of Wave Phenomena, Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, V.O., Bol'shoy pr. 61, St. Petersburg 199178, Russian Federation 
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Nikolay Kuznetsov. Uniqueness in the water-wave problem for bodies intersecting the free surface at arbitrary angles. Comptes Rendus. Mécanique, Volume 332 (2004) no. 1, pp. 73-78. doi : 10.1016/j.crme.2003.10.008. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2003.10.008/

[1] F. John On the motion of floating bodies. II, Comm. Pure Appl. Math., Volume 3 (1950), pp. 45-101

[2] M.J. Simon; F. Ursell Uniqueness in linearized two-dimensional water-wave problems, J. Fluid Mech., Volume 148 (1984), pp. 137-154

[3] N. Kuznetsov; V. Maz'ya; B. Vainberg Linear Water Waves: A Mathematical Approach, Cambridge University Press, 2002

[4] M. McIver An example of non-uniqueness in the two-dimensional linear water-wave problem, J. Fluid Mech., Volume 315 (1996), pp. 257-266

[5] F. Ursell Some Unsolved and Unfinished Problems in the Theory of Waves, Wave Asymptotics, Cambridge University Press, 1992

[6] P. Moon; D.E. Spencer Field Theory Handbook, Springer-Verlag, 1971

[7] P.M. Morse; H. Feshbach Methods of Theoretical Physics, Part II, McGraw-Hill, 1953

[8] B.R. Vainberg; V.G. Maz'ya On the problem of the steady state oscillations of a fluid layer of variable depth, Trans. Moscow Math. Soc., Volume 28 (1973), pp. 56-73

[9] M. McIver Uniqueness and trapped modes for a symmetric structure, Proc. of the 14th Int. Workshop on Water Waves and Floating Bodies, University of Michigan, Ann Arbor, 1999

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