메뉴 건너뛰기




Volumn 62, Issue 3, 2007, Pages 453-473

Mathematical aspects of surface water waves

Author keywords

[No Author keywords available]

Indexed keywords


EID: 35748961701     PISSN: 00360279     EISSN: 14684829     Source Type: Journal    
DOI: 10.1070/RM2007v062n03ABEH004413     Document Type: Conference Paper
Times cited : (16)

References (58)
  • 1
    • 34250447917 scopus 로고
    • Stability of periodic waves of finite amplitude on the surface of a deep fluid
    • V. E. Zakharov, "Stability of periodic waves of finite amplitude on the surface of a deep fluid", J. Appl. Mech. Tech. Phys. 9:2 (1968), 190-194.
    • (1968) J. Appl. Mech. Tech. Phys , vol.9 , Issue.2 , pp. 190-194
    • Zakharov, V.E.1
  • 2
    • 0002686768 scopus 로고
    • Numerical simulation of gravity waves
    • W. Craig and C. Sulem, "Numerical simulation of gravity waves", J. Comput. Phys. 108:1 (1993), 73-83.
    • (1993) J. Comput. Phys , vol.108 , Issue.1 , pp. 73-83
    • Craig, W.1    Sulem, C.2
  • 3
    • 84974513241 scopus 로고
    • A variational principle for a fluid with a free surface
    • J. C. Luke, "A variational principle for a fluid with a free surface", J. Fluid Mech. 27 (1967), 395-397.
    • (1967) J. Fluid Mech , vol.27 , pp. 395-397
    • Luke, J.C.1
  • 4
    • 0344939482 scopus 로고
    • Non local Cauchy problems in fluid dynamics
    • Nice, Gauthier- Villars, Paris
    • L. V. Ovsiannikov, "Non local Cauchy problems in fluid dynamics", Actes du congrès international des mathématiciens (Nice, 1970), vol. 3, Gauthier- Villars, Paris 1971, pp. 137-142.
    • (1970) Actes du congrès international des mathématiciens , vol.3 , pp. 137-142
    • Ovsiannikov, L.V.1
  • 5
    • 0000306561 scopus 로고
    • The Cauchy-Poisson problem
    • [V. I. Nalimov, "The Cauchy-Poisson problem", Continuum Dynamics 18 (1974), 104-210.]
    • (1974) Continuum Dynamics , vol.18 , pp. 104-210
    • Nalimov, I.1
  • 6
    • 0040325565 scopus 로고
    • Sur les ondes de surface de l'eau avec une justification mathématique des équations des ondes en eau peu profonde
    • T. Kano and T. Nishida, "Sur les ondes de surface de l'eau avec une justification mathématique des équations des ondes en eau peu profonde", J. Math. Kyoto Univ. 19:2 (1979), 335-370.
    • (1979) J. Math. Kyoto Univ , vol.19 , Issue.2 , pp. 335-370
    • Kano, T.1    Nishida, T.2
  • 7
    • 85164641269 scopus 로고    scopus 로고
    • M. Shinbrot, The initial value problem for surface waves under gravity. I. The simplest case, Indiana Univ. Math. J. 25:3 (1976), 281-300.
    • M. Shinbrot, "The initial value problem for surface waves under gravity. I. The simplest case", Indiana Univ. Math. J. 25:3 (1976), 281-300.
  • 8
    • 85164642883 scopus 로고    scopus 로고
    • J. Reeder and M. Shinbrot, The initial value problem for surface waves under gravity. II. The simplest 3-dimensional case, Indiana Univ. Math. J. 25:11 (1976), 1049-1071.
    • J. Reeder and M. Shinbrot, "The initial value problem for surface waves under gravity. II. The simplest 3-dimensional case", Indiana Univ. Math. J. 25:11 (1976), 1049-1071.
  • 9
    • 0018433448 scopus 로고
    • The initial value problem for surface waves under gravity. III. Uniformly analytic initial domains
    • J. Reeder and M. Shinbrot, "The initial value problem for surface waves under gravity. III. Uniformly analytic initial domains", J. Math. Anal. Appl. 67:2 (1979), 340-391.
    • (1979) J. Math. Anal. Appl , vol.67 , Issue.2 , pp. 340-391
    • Reeder, J.1    Shinbrot, M.2
  • 10
    • 0038247451 scopus 로고
    • Finite time analyticity for the two- and three-dimensional Kelvin-Helmholtz instability
    • C. Sulem, P.-L. Sulem, C. Bardos, and U. Frisch, "Finite time analyticity for the two- and three-dimensional Kelvin-Helmholtz instability", Comm. Math. Phys. 80:4 (1981), 485-516.
    • (1981) Comm. Math. Phys , vol.80 , Issue.4 , pp. 485-516
    • Sulem, C.1    Sulem, P.-L.2    Bardos, C.3    Frisch, U.4
  • 11
    • 85009585833 scopus 로고
    • Gravity waves on the free surface of an incompressible perfect fluid of finite depth
    • H. Yosihara, "Gravity waves on the free surface of an incompressible perfect fluid of finite depth", Publ. Res. Inst. Math. Sci. 18:1 (1982), 49-96.
    • (1982) Publ. Res. Inst. Math. Sci , vol.18 , Issue.1 , pp. 49-96
    • Yosihara, H.1
  • 12
    • 0000375767 scopus 로고
    • Capillary-gravity waves for an incompressible ideal fluid, J
    • H. Yosihara, "Capillary-gravity waves for an incompressible ideal fluid", J. Math. Kyoto Univ. 23:4 (1983), 649-694.
    • (1983) Math. Kyoto Univ , vol.23 , Issue.4 , pp. 649-694
    • Yosihara, H.1
  • 13
    • 0001688084 scopus 로고
    • An existence theory for water waves and the Boussinesq and Korteweg-de Vries scaling limits
    • 7871003
    • W. Craig, "An existence theory for water waves and the Boussinesq and Korteweg-de Vries scaling limits'", Comm. Partial Differential Equations 10:8 (1985), 7871003.
    • (1985) Comm. Partial Differential Equations , vol.10 , pp. 8
    • Craig, W.1
  • 14
    • 0034364719 scopus 로고    scopus 로고
    • The long-wave limit for the water wave problem. I. The case of zero surface tension
    • M. Shinbrot and C. E. Wayne, "The long-wave limit for the water wave problem. I. The case of zero surface tension", Comm. Pure Appl. Math. 53:12 (2000), 1475-1535.
    • (2000) Comm. Pure Appl. Math , vol.53 , Issue.12 , pp. 1475-1535
    • Shinbrot, M.1    Wayne, C.E.2
  • 15
    • 0036012969 scopus 로고    scopus 로고
    • The rigorous approximation of long-wavelength capillary-gravity waves
    • M. Shinbrot and C. E. Wayne, "The rigorous approximation of long-wavelength capillary-gravity waves", Arch. Ration. Mech. Anal. 162:3 (2002), 247-285.
    • (2002) Arch. Ration. Mech. Anal , vol.162 , Issue.3 , pp. 247-285
    • Shinbrot, M.1    Wayne, C.E.2
  • 16
    • 0031506263 scopus 로고    scopus 로고
    • Well-posedness in Sobolev spaces of the full water wave problem in 2-D
    • S. Wu, "Well-posedness in Sobolev spaces of the full water wave problem in 2-D", Invent. Math. 130:1 (1997), 39-72.
    • (1997) Invent. Math , vol.130 , Issue.1 , pp. 39-72
    • Wu, S.1
  • 17
    • 0033446356 scopus 로고    scopus 로고
    • Well-posedness in Sobolev spaces of the full water wave problem in 3-D
    • S. Wu, "Well-posedness in Sobolev spaces of the full water wave problem in 3-D", J. Amer. Math. Soc. 12:2 (1999), 445-495.
    • (1999) J. Amer. Math. Soc , vol.12 , Issue.2 , pp. 445-495
    • Wu, S.1
  • 18
    • 22544482964 scopus 로고    scopus 로고
    • Well-posedness of the water-waves equations
    • D. Lannes, "Well-posedness of the water-waves equations", J. Amer. Math. Soc. 18:3 (2005), 605-654.
    • (2005) J. Amer. Math. Soc , vol.18 , Issue.3 , pp. 605-654
    • Lannes, D.1
  • 19
    • 0001647402 scopus 로고
    • Détermination rigoureuse des ondes permanentes d'ampleur finie
    • T. Levi-Civita, "Détermination rigoureuse des ondes permanentes d'ampleur finie", Math. Ann. 93:1 (1925), 264-314.
    • (1925) Math. Ann , vol.93 , Issue.1 , pp. 264-314
    • Levi-Civita, T.1
  • 20
    • 85164654259 scopus 로고    scopus 로고
    • Russian source
    • Russian source
  • 21
    • 34548460933 scopus 로고
    • The exact theory of steady state waves on the surface of a heavy liquid
    • No 813, Univ. of Wisconsin, Madison
    • English transl., A. I. Nekrasov, The exact theory of steady state waves on the surface of a heavy liquid, MRC Technical Report No 813, Univ. of Wisconsin, Madison 1967.
    • (1967) MRC Technical Report
    • English transl, A.1    Nekrasov, I.2
  • 22
    • 0001534794 scopus 로고
    • Détermination rigoureuse des ondes irrotationelles périodiques dans un canal à profondeur finie
    • D. Struik, "Détermination rigoureuse des ondes irrotationelles périodiques dans un canal à profondeur finie", Math. Ann. 95:1 (1926), 595-634.
    • (1926) Math. Ann , vol.95 , Issue.1 , pp. 595-634
    • Struik, D.1
  • 23
    • 85164650100 scopus 로고    scopus 로고
    • AH CCCP 41:7 (1943), 289-291.
    • AH CCCP 41:7 (1943), 289-291.
  • 25
    • 44649175376 scopus 로고
    • The existence of solitary waves
    • K. O. Friedrichs and D. H. Hyers, "The existence of solitary waves", Comm. Pure Appl. Math. 7:3 (1954), 517-550.
    • (1954) Comm. Pure Appl. Math , vol.7 , Issue.3 , pp. 517-550
    • Friedrichs, K.O.1    Hyers, D.H.2
  • 26
    • 0034368951 scopus 로고    scopus 로고
    • On the motion of the free surface of a liquid
    • D. Christodoulou and H. Lindblad, "On the motion of the free surface of a liquid", Comm. Pure Appl. Math. 53:12 (2000), 1536-1602.
    • (2000) Comm. Pure Appl. Math , vol.53 , Issue.12 , pp. 1536-1602
    • Christodoulou, D.1    Lindblad, H.2
  • 27
    • 26044448758 scopus 로고    scopus 로고
    • Well-posedness for the motion of an incompressible liquid with free surface boundary
    • H. Lindblad, "Well-posedness for the motion of an incompressible liquid with free surface boundary", Ann. of Math. (2) 162:1 (2005), 109-194.
    • (2005) Ann. of Math. (2) , vol.162 , Issue.1 , pp. 109-194
    • Lindblad, H.1
  • 28
    • 0011555392 scopus 로고
    • The equations of motion of a perfect fluid with free boundary are not well posed
    • D. Ebin, "The equations of motion of a perfect fluid with free boundary are not well posed", Comm. Partial Differential Equations 12:10 (1987), 1175-1201.
    • (1987) Comm. Partial Differential Equations , vol.12 , Issue.10 , pp. 1175-1201
    • Ebin, D.1
  • 29
    • 0020292888 scopus 로고
    • Hamiltonian structure, symmetries and conservation laws for water waves
    • T. B. Benjamin and P. J. Olver, "Hamiltonian structure, symmetries and conservation laws for water waves", J. Fluid Mech. 125 (1982), 137-185.
    • (1982) J. Fluid Mech , vol.125 , pp. 137-185
    • Benjamin, T.B.1    Olver, P.J.2
  • 30
    • 69549102728 scopus 로고
    • Water waves and Friedrichs expansion
    • Hiroshima, North-Holland Math. Stud, North-Holland, Amsterdam
    • T. Kano and T. Nishida, "Water waves and Friedrichs expansion", Recent topics in nonlinear PDE (Hiroshima, 1983), North-Holland Math. Stud., vol. 98, North-Holland, Amsterdam 1984, pp. 39-57.
    • (1983) Recent topics in nonlinear PDE , vol.98 , pp. 39-57
    • Kano, T.1    Nishida, T.2
  • 31
    • 84972562218 scopus 로고
    • A mathematical justification for Korteweg-de Vries equation and Boussinesq equation of water surface waves
    • T. Kano and T. Nishida, "A mathematical justification for Korteweg-de Vries equation and Boussinesq equation of water surface waves", Osaka J. Math. 23:2 (1986), 389-413.
    • (1986) Osaka J. Math , vol.23 , Issue.2 , pp. 389-413
    • Kano, T.1    Nishida, T.2
  • 32
    • 33744803750 scopus 로고    scopus 로고
    • Corrections to the KdV approximation for water waves
    • J. D. Wright, "Corrections to the KdV approximation for water waves", SIAM J. Math. Anal. 37:4 (2005), 1161-1206.
    • (2005) SIAM J. Math. Anal , vol.37 , Issue.4 , pp. 1161-1206
    • Wright, J.D.1
  • 33
    • 27944474754 scopus 로고    scopus 로고
    • Long wave approximations for water waves
    • J. Bona, Th. Colin, and D. Lannes, "Long wave approximations for water waves", Arch-Ration. Mech. Anal. 178:3 (2005), 373-410.
    • (2005) Arch-Ration. Mech. Anal , vol.178 , Issue.3 , pp. 373-410
    • Bona, J.1    Colin, T.2    Lannes, D.3
  • 34
    • 0000784514 scopus 로고
    • Nonlinear modulation of gravity waves: A rigorous approach
    • W. Craig, C. Sulem, and P.-L. Sulem, "Nonlinear modulation of gravity waves: a rigorous approach", Nonlinearity 5:2 (1992), 497-522.
    • (1992) Nonlinearity , vol.5 , Issue.2 , pp. 497-522
    • Craig, W.1    Sulem, C.2    Sulem, P.-L.3
  • 35
    • 0001654990 scopus 로고    scopus 로고
    • The modulational regime of three-dimensional water waves and the Davey-Stewartson system
    • W. Craig, U. Schanz, and C. Sulem, "The modulational regime of three-dimensional water waves and the Davey-Stewartson system", Ann. Inst. H. Poincaré Anal. Non Linéaire 14:5 (1997), 615-667.
    • (1997) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.14 , Issue.5 , pp. 615-667
    • Craig, W.1    Schanz, U.2    Sulem, C.3
  • 36
    • 0028443419 scopus 로고
    • Hamiltonian long-wave approximations to the water-wave problem
    • W. Craig and M. Groves, "Hamiltonian long-wave approximations to the water-wave problem", Wave Motion 19:4 (1994), 367-389.
    • (1994) Wave Motion , vol.19 , Issue.4 , pp. 367-389
    • Craig, W.1    Groves, M.2
  • 38
    • 0039965249 scopus 로고
    • Existenzbeweis für cnoidal waves unter Berücksichtigung der Oberflächenspannung
    • E. Zeidler, "Existenzbeweis für cnoidal waves unter Berücksichtigung der Oberflächenspannung", Arch. Rational Mech. Anal. 41:2 (1971), 81-107.
    • (1971) Arch. Rational Mech. Anal , vol.41 , Issue.2 , pp. 81-107
    • Zeidler, E.1
  • 39
    • 0019656759 scopus 로고
    • On solitary water-waves of finite amplitude
    • C. J. Amick and J. F. Toland, "On solitary water-waves of finite amplitude", Arch. Ration. Mech. Anal. 76:1 (1981), 9-95.
    • (1981) Arch. Ration. Mech. Anal , vol.76 , Issue.1 , pp. 9-95
    • Amick, C.J.1    Toland, J.F.2
  • 40
    • 0000166670 scopus 로고
    • On the Stokes conjecture for the wave of extreme form
    • C. J. Amick, L. E. Fraenkel, and J. F. Toland, "On the Stokes conjecture for the wave of extreme form", Acta Math. 148:1 (1982), 193-214.
    • (1982) Acta Math , vol.148 , Issue.1 , pp. 193-214
    • Amick, C.J.1    Fraenkel, L.E.2    Toland, J.F.3
  • 41
    • 0022284536 scopus 로고
    • Nonlinear wave motion and homoclinic bifurcation
    • Lyngby, North-Holland, Amsterdam
    • K. Kirchgässner, "Nonlinear wave motion and homoclinic bifurcation", Theoretical and applied mechanics (Lyngby, 1984), North-Holland, Amsterdam 1985, pp. 219-231.
    • (1984) Theoretical and applied mechanics , pp. 219-231
    • Kirchgässner, K.1
  • 42
    • 0003540692 scopus 로고
    • Hamiltonian and Lagrangian flows on center manifolds. With applications to elliptic variational problems
    • Springer-Verlag, Berlin
    • A. Mielke, Hamiltonian and Lagrangian flows on center manifolds. With applications to elliptic variational problems, Lecture Notes in Math., vol. 1489, Springer-Verlag, Berlin 1991.
    • (1991) Lecture Notes in Math , vol.1489
    • Mielke, A.1
  • 43
    • 0000226991 scopus 로고
    • Three-dimensional, nonlinear wave interaction in water of constant depth
    • J. Reeder and M. Shinbrot, "Three-dimensional, nonlinear wave interaction in water of constant depth", Nonlinear Anal. 5:3 (1981), 303-323.
    • (1981) Nonlinear Anal , vol.5 , Issue.3 , pp. 303-323
    • Reeder, J.1    Shinbrot, M.2
  • 44
    • 0034550889 scopus 로고    scopus 로고
    • Travelling two and three dimensional capillary gravity water waves
    • W. Craig and D. Nicholls, "Travelling two and three dimensional capillary gravity water waves", SIAM J. Math. Anal. 32:2 (2000), 323-359.
    • (2000) SIAM J. Math. Anal , vol.32 , Issue.2 , pp. 323-359
    • Craig, W.1    Nicholls, D.2
  • 45
    • 0035610302 scopus 로고    scopus 로고
    • Nash-Moser theory for standing water waves
    • P. I. Plotnikov and J. F. Toland, "Nash-Moser theory for standing water waves", Arch. Ration. Mech. Anal. 159:1 (2001), 1-83.
    • (2001) Arch. Ration. Mech. Anal , vol.159 , Issue.1 , pp. 1-83
    • Plotnikov, P.I.1    Toland, J.F.2
  • 46
    • 23944524329 scopus 로고    scopus 로고
    • Standing waves on an infinitely deep perfect fluid under gravity
    • G. Iooss, P. I. Plotnikov, and J. F. Toland, "Standing waves on an infinitely deep perfect fluid under gravity", Arch. Ration. Mech. Anal. 177:3 (2005), 367-478.
    • (2005) Arch. Ration. Mech. Anal , vol.177 , Issue.3 , pp. 367-478
    • Iooss, G.1    Plotnikov, P.I.2    Toland, J.F.3
  • 48
    • 0037107483 scopus 로고    scopus 로고
    • Non-existence of solitary water waves in three dimensions
    • W. Craig, "Non-existence of solitary water waves in three dimensions", R. Soc. Lond. Philos. Trans. Ser. A. Math. Phys. Eng. Sci. 360:1799 (2002), 2127-2135.
    • (2002) R. Soc. Lond. Philos. Trans. Ser. A. Math. Phys. Eng. Sci , vol.360 , Issue.1799 , pp. 2127-2135
    • Craig, W.1
  • 49
    • 84969657666 scopus 로고    scopus 로고
    • Fully localised solitary-wave solutions of the three-dimensional gravity-capillary water-wave problem
    • to appear
    • M. Groves and S.-M. Sun, "Fully localised solitary-wave solutions of the three-dimensional gravity-capillary water-wave problem", Arch. Ration. Mech. Anal. (to appear).
    • Arch. Ration. Mech. Anal
    • Groves, M.1    Sun, S.-M.2
  • 50
    • 85164637649 scopus 로고    scopus 로고
    • Russian source
    • Russian source
  • 51
    • 85164639305 scopus 로고    scopus 로고
    • English transl., P.I. Plotnikov, Nonuniqueness of solutions of a problem on solitary waves, and bifurcations of critical points of smooth functionals, Math. USSR-Izv. 38:2 (1992), 333-357.
    • English transl., P.I. Plotnikov, "Nonuniqueness of solutions of a problem on solitary waves, and bifurcations of critical points of smooth functionals", Math. USSR-Izv. 38:2 (1992), 333-357.
  • 53
    • 2342508836 scopus 로고
    • On the non-linear energy transfer in a gravity-wave spectrum. I. General theory
    • K. Hasselmann, "On the non-linear energy transfer in a gravity-wave spectrum. I. General theory", J. Fluid Mech. 12 (1962), 481-500.
    • (1962) J. Fluid Mech , vol.12 , pp. 481-500
    • Hasselmann, K.1
  • 54
    • 85164639517 scopus 로고    scopus 로고
    • Russian source
    • Russian source
  • 56
    • 85164641085 scopus 로고    scopus 로고
    • V. E. Zakharov, V. S. L'vov, and G. Falkovich, Kolmogorov spectra of turbulence. I. Wave turbulence, Springer-Verlag, Berlin-New York 1992.
    • V. E. Zakharov, V. S. L'vov, and G. Falkovich, Kolmogorov spectra of turbulence. I. Wave turbulence, Springer-Verlag, Berlin-New York 1992.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.