A discussion on Neumann–Kelvin's model for progressive water waves

References

• Kelvin (Sir Thomson) , L . 1887 . On the waves produced by a single input in water of any depth, or in a dispersive medium . Proc. Roy. Soc. Lond. A , 42 : 80 – 85 .
   Google Scholar
• Livshits , M and Maz'ya , V . 1997 . Solvability of the two-dimensional Neumann–Kelvin's problem for a submerged circular cylinder . Appl. Anal. , 64 : 1 – 5 .
   Google Scholar
• Stoker , JJ . 1957 . “ Water Waves ” . In Pure and Applied Mathematics , Vol. IV , New York : Inter Science publishers, Inc. .
   Google Scholar
• Doutreleau , Y . 1995 . “ Résonances pour le problème de Neumann–Kelvin tridimensionnel dans le cas d'un corps immergé ” . In 5th Journées de l'Hydrodynamique , Mars : Rouen .
   Google Scholar
• Chen , X . 2001 . On the singular and highly oscillatory properties of the Green function for ship motions . J. Fluid Mechs. , 445 : 77 – 91 .
   Google Scholar
• Campana , EF and Iafrati , A . July 2002 . Direct numerical simulation of surface tension dominated and non-dominated breaking waves, 24th Symposium on Naval Hydrodynamics , July , Japan : Fukuoka .
   Google Scholar
• Moak , DS . 1981 . The q-analogue of the Laguerre polynomials . J. Math. Anal. Appl. , 81 : 20 – 47 .
   Web of Science ®Google Scholar
• Destuynder , Ph and Fabre , C . 2008 . A modelling of springing, whipping and slamming for ships . Commun. Pure Appl. Anal. , 8 ( 1 ) : 209 – 228 .
   Google Scholar
• Gazzola , Th , Korobkin , A , Malenica , S and Scolan , YM . Three-dimensional Wagner problem using variational inequalities . Proceedings of the 20th International Workshop on Water Waves and Floating Bodies, Longyearbyen, Norway, pp. 77–81, 2005 ,
   Google Scholar
• Gazzola , Th . 2007 . Modélisation du phénomène de tossage pour les bateaux , Thèse de l'Ecole Centrale de Paris .
   Google Scholar
• Artiles , W and Nachbin , A . 2004 . Asymptotic nonlinear wave modeling through the Dirichlet to Neumann operator, Methods Appl. Anal. 11(3) (2004) 001018
   Google Scholar
• Lannes , D . 2005 . Well posedness of the water waves equations . J. Amer. Math. Soc. , 13 ( 3 ) : 605 – 654 .
   Google Scholar
• Craig , W and Sulem , C . 1993 . Numerical simulation of gravity waves . J. Comput. Phys. , 108 ( 1 ) : 73 – 83 .
   Google Scholar
• Coifman , R and Meyer , Y . 1985 . “ Nonlinear Harmonic Analysis and Analytic Dependence ” . In Pseudodifferential Operators and Applications , Providence, RI : AMS .
   Google Scholar
• Necas , J . 1967 . Les Méthodes Directes en Théorie des Équations Elliptiques , Paris : Masson .
   Google Scholar
• Grisvard , P . 1992 . Singularities in Boundary Value Problems , Paris : Masson .
   Google Scholar
• Borsuk , M and Kondratiev , V . 2006 . Elliptic Boundary Value Problems of Second Order in Piecewise Smooth Domains , Amsterdam : North Holland, Mathematical Library .
   Google Scholar
• Adams , R . 1975 . Sobolev Spaces , New York : Academic Press .
   Google Scholar
• Lions , JL and Magenes , E . 1968 . Problèmes aux Limites Non-homogènes et Applications, Tome 1 , Paris : Dunod .
   Google Scholar
• Duvaut , G . 1990 . Mécanique des Milieux Continus , Paris : Dunod .
   Google Scholar
• Landau , L and Lifchitz , E . 2007 . “ Mécanique des fluides ” . In J. Eng. Math. 58 (2007) 121 – 139 .
   Google Scholar
• Raviart , PA and Thomas , JM . 1983 . Introduction à l'Analyse Numérique des Équations aux Dérivées Partielles , Paris : Masson .
   Google Scholar
• Chen , X . 14–17 April 2002 . “ Role of the surface tension in modelling ship waves ” . In Proceedings of the 17th International Workshop on Water Waves and Floating Bodies , Edited by: Rayney , RC and Lee , SF . 14–17 April , 25 – 28 . UK : Peterhouse, Cambridge .
   Google Scholar
• Lions , JL . 1969 . Quelques Méthodes de Résolution des Problèmes aux Limites Non-linéaires , Paris : Dunod .
   Google Scholar
• Kirchgassner , K . 1988 . Nonlinear resonant surface waves and homoclinic bifurcation . Adv. Appl. Math. , 26 : 135181
   Google Scholar