메뉴 건너뛰기




Volumn 175, Issue 2, 2012, Pages 691-754

Global solutions for the gravity water waves equation in dimension 3

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84857870242     PISSN: 0003486X     EISSN: None     Source Type: Journal    
DOI: 10.4007/annals.2012.175.2.6     Document Type: Article
Times cited : (320)

References (29)
  • 1
    • 34547194744 scopus 로고    scopus 로고
    • Well-posedness of 3D vortex sheets with surface tension
    • D. M. Ambrose and N. Masmoudi, Well-posedness of 3D vortex sheets with surface tension, Commun. Math. Sci. 5 (2007), 391-430.
    • (2007) Commun. Math. Sci. , vol.5 , pp. 391-430
    • Ambrose, D.M.1    Masmoudi, N.2
  • 2
    • 67249144683 scopus 로고    scopus 로고
    • The zero surface tension limit of three-dimensional water waves
    • D. M. Ambrose and N. Masmoudi, The zero surface tension limit of three-dimensional water waves, Indiana Univ. Math. J. 58 (2009), 479-521.
    • (2009) Indiana Univ. Math. J. , vol.58 , pp. 479-521
    • Ambrose, D.M.1    Masmoudi, N.2
  • 3
    • 84990576574 scopus 로고
    • Growth rates for the linearized motion of fluid interfaces away from equilibrium
    • J. T. Beale, T. Y. Hou, and J. S. Lowengrub, Growth rates for the linearized motion of fluid interfaces away from equilibrium, Comm. Pure Appl. Math. 46 (1993), 1269-1301.
    • (1993) Comm. Pure Appl. Math. , vol.46 , pp. 1269-1301
    • Beale, J.T.1    Hou, T.Y.2    Lowengrub, J.S.3
  • 4
    • 84990602498 scopus 로고
    • Global solutions of nonlinear hyperbolic equations for small initial data
    • D. Christodoulou, Global solutions of nonlinear hyperbolic equations for small initial data, Comm. Pure Appl. Math. 39 (1986), 267-282.
    • (1986) Comm. Pure Appl. Math. , vol.39 , pp. 267-282
    • Christodoulou, D.1
  • 5
    • 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 (2000), 1536-1602.
    • (2000) Comm. Pure Appl. Math. , vol.53 , pp. 1536-1602
    • Christodoulou, D.1    Lindblad, H.2
  • 6
    • 0001923237 scopus 로고
    • Au delà des Opérateurs Pseudo-Différentiels
    • Société Mathématique de France, Paris
    • R. R. Coifman and Y. Meyer, Au delà des Opérateurs Pseudo-Différentiels, Astérisque 57, Société Mathématique de France, Paris, 1978.
    • (1978) Astérisque , vol.57
    • Coifman, R.R.1    Meyer, Y.2
  • 7
    • 34548446988 scopus 로고    scopus 로고
    • Well-posedness of the free-surface incompressible Euler equations with or without surface tension
    • D. Coutand and S. Shkoller, Well-posedness of the free-surface incompressible Euler equations with or without surface tension, J. Amer. Math. Soc. 20 (2007), 829-930.
    • (2007) J. Amer. Math. Soc. , vol.20 , pp. 829-930
    • Coutand, D.1    Shkoller, S.2
  • 8
    • 0001688084 scopus 로고
    • An existence theory for water waves and the Boussinesq and Kortewegde Vries scaling limits
    • W. Craig, An existence theory for water waves and the Boussinesq and Kortewegde Vries scaling limits, Comm. Partial Differential Equations 10 (1985), 787-1003.
    • (1985) Comm. Partial Differential Equations , vol.10 , pp. 787-1003
    • Craig, W.1
  • 9
    • 0034550889 scopus 로고    scopus 로고
    • Traveling two and three dimensional capillary gravity water waves
    • W. Craig and D. P. Nicholls, Traveling two and three dimensional capillary gravity water waves, SIAM J. Math. Anal. 32 (2000), 323-359.
    • (2000) SIAM J. Math. Anal. , vol.32 , pp. 323-359
    • Craig, W.1    Nicholls, D.P.2
  • 11
  • 12
    • 84990602599 scopus 로고
    • Uniform decay estimates and the Lorentz invariance of the classical wave equation
    • S. Klainerman, Uniform decay estimates and the Lorentz invariance of the classical wave equation, Comm. Pure Appl. Math. 38 (1985), 321-332.
    • (1985) Comm. Pure Appl. Math. , vol.38 , pp. 321-332
    • Klainerman, S.1
  • 13
    • 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 (2005), 605-654.
    • (2005) J. Amer. Math. Soc. , vol.18 , pp. 605-654
    • Lannes, D.1
  • 14
    • 36248997661 scopus 로고    scopus 로고
    • Paraproducts with flag singularities. I. A case study
    • C. Muscalu, Paraproducts with flag singularities. I. A case study, Rev. Mat. Iberoam. 23 (2007), 705-742.
    • (2007) Rev. Mat. Iberoam. , vol.23 , pp. 705-742
    • Muscalu, C.1
  • 15
    • 0000306561 scopus 로고
    • The Cauchy-Poisson problem
    • V. I. Nalimov, The Cauchy-Poisson problem, Dinamika Splošn. Sredy (1974), 104-210, 254.
    • (1974) Dinamika Splošn. Sredy , vol.104-210 , pp. 254
    • Nalimov, V.I.1
  • 16
    • 0036951682 scopus 로고    scopus 로고
    • Free boundary problem for an incompressible ideal fluid with surface tension
    • M. Ogawa and A. Tani, Free boundary problem for an incompressible ideal fluid with surface tension, Math. Models Methods Appl. Sci. 12 (2002), 1725-1740.
    • (2002) Math. Models Methods Appl. Sci. , vol.12 , pp. 1725-1740
    • Ogawa, M.1    Tani, A.2
  • 17
    • 0036012969 scopus 로고    scopus 로고
    • The rigorous approximation of long-wavelength capillary-gravity waves
    • G. Schneider and C. E. Wayne, The rigorous approximation of long-wavelength capillary-gravity waves, Arch. Ration. Mech. Anal. 162 (2002), 247-285.
    • (2002) Arch. Ration. Mech. Anal. , vol.162 , pp. 247-285
    • Schneider, G.1    Wayne, C.E.2
  • 18
    • 84990623722 scopus 로고
    • Normal forms and quadratic nonlinear Klein-Gordon equations
    • J. Shatah, Normal forms and quadratic nonlinear Klein-Gordon equations, Comm. Pure Appl. Math. 38 (1985), 685-696.
    • (1985) Comm. Pure Appl. Math. , vol.38 , pp. 685-696
    • Shatah, J.1
  • 19
    • 52349104032 scopus 로고    scopus 로고
    • Geometry and a priori estimates for free boundary problems of the Euler equation
    • J. Shatah and C. Zeng, Geometry and a priori estimates for free boundary problems of the Euler equation, Comm. Pure Appl. Math. 61 (2008), 698-744.
    • (2008) Comm. Pure Appl. Math. , vol.61 , pp. 698-744
    • Shatah, J.1    Zeng, C.2
  • 20
    • 78751704957 scopus 로고    scopus 로고
    • Local well-posedness for fluid interface problems
    • J. Shatah and C. Zeng, Local well-posedness for fluid interface problems, Arch. Ration. Mech. Anal. 199 (2011), 653-705.
    • (2011) Arch. Ration. Mech. Anal. , vol.199 , pp. 653-705
    • Shatah, J.1    Zeng, C.2
  • 21
    • 0003552286 scopus 로고
    • Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Math. Series
    • Princeton Univ. Press, Princeton, NJ
    • E. M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Math. Series 43, Princeton Univ. Press, Princeton, NJ, 1993.
    • (1993) , vol.43
    • Stein, E.M.1
  • 24
    • 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 (1997), 39-72.
    • (1997) Invent. Math. , vol.130 , pp. 39-72
    • Wu, S.1
  • 25
    • 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 (1999), 445-495.
    • (1999) J. Amer. Math. Soc. , vol.12 , pp. 445-495
    • Wu, S.1
  • 26
    • 67650433790 scopus 로고    scopus 로고
    • Almost global wellposedness of the 2-D full water wave problem
    • to appear
    • S. Wu, Almost global wellposedness of the 2-D full water wave problem, 2009, Invent. Math., to appear.
    • (2009) Invent. Math.
    • Wu, S.1
  • 28
    • 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 (1982), 49-96.
    • (1982) Publ. Res. Inst. Math. Sci. , vol.18 , pp. 49-96
    • Yosihara, H.1
  • 29
    • 52349109943 scopus 로고    scopus 로고
    • On the free boundary problem of three-dimensional incompressible Euler equations
    • P. Zhang and Z. Zhang, On the free boundary problem of three-dimensional incompressible Euler equations, Comm. Pure Appl. Math. 61 (2008).
    • (2008) Comm. Pure Appl. Math. , vol.61
    • Zhang, P.1    Zhang, Z.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.