메뉴 건너뛰기




Volumn 254, Issue 3, 2013, Pages 1006-1096

Existence and conditional energetic stability of three-dimensional fully localised solitary gravity-capillary water waves

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84870372052     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2012.10.007     Document Type: Article
Times cited : (43)

References (33)
  • 1
    • 0018480221 scopus 로고
    • On the evolution of packets of water waves
    • Ablowitz M.J., Segur H. On the evolution of packets of water waves. J. Fluid Mech. 1979, 92:691-715.
    • (1979) J. Fluid Mech. , vol.92 , pp. 691-715
    • Ablowitz, M.J.1    Segur, H.2
  • 3
    • 79959880152 scopus 로고    scopus 로고
    • On the water-wave equations with surface tension
    • Alazard T., Burq N., Zuily C. On the water-wave equations with surface tension. Duke Math. J. 2011, 158:413-499.
    • (2011) Duke Math. J. , vol.158 , pp. 413-499
    • Alazard, T.1    Burq, N.2    Zuily, C.3
  • 4
    • 0003372381 scopus 로고
    • Lectures on nonlinear wave motion
    • Amer. Math. Soc.
    • Benjamin T.B. Lectures on nonlinear wave motion. Lectures in Appl. Math. 1974, vol. 15:3-47. Amer. Math. Soc.
    • (1974) Lectures in Appl. Math. , vol.15 , pp. 3-47
    • Benjamin, T.B.1
  • 5
    • 0020292888 scopus 로고
    • Hamiltonian structure, symmetries and conservation laws for water waves
    • Benjamin T.B., Olver P.J. Hamiltonian structure, symmetries and conservation laws for water waves. J. Fluid Mech. 1982, 125:137-185.
    • (1982) J. Fluid Mech. , vol.125 , pp. 137-185
    • Benjamin, T.B.1    Olver, P.J.2
  • 6
    • 0034923110 scopus 로고    scopus 로고
    • The generation and evolution of lump solitary waves in surface-tension-dominated flows
    • Berger K.M., Milewski P.A. The generation and evolution of lump solitary waves in surface-tension-dominated flows. SIAM J. Appl. Math. 2000, 61:731-750.
    • (2000) SIAM J. Appl. Math. , vol.61 , pp. 731-750
    • Berger, K.M.1    Milewski, P.A.2
  • 7
    • 3142676320 scopus 로고    scopus 로고
    • Existence and conditional energetic stability of capillary-gravity solitary water waves by minimisation
    • Buffoni B. Existence and conditional energetic stability of capillary-gravity solitary water waves by minimisation. Arch. Ration. Mech. Anal. 2004, 173:25-68.
    • (2004) Arch. Ration. Mech. Anal. , vol.173 , pp. 25-68
    • Buffoni, B.1
  • 8
    • 2942612628 scopus 로고    scopus 로고
    • Existence by minimisation of solitary water waves on an ocean of infinite depth
    • Buffoni B. Existence by minimisation of solitary water waves on an ocean of infinite depth. Ann. Inst. H. Poincaré Anal. Non Linéaire 2004, 21:503-516.
    • (2004) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.21 , pp. 503-516
    • Buffoni, B.1
  • 9
    • 33947385263 scopus 로고    scopus 로고
    • Conditional energetic stability of gravity solitary waves in the presence of weak surface tension
    • Buffoni B. Conditional energetic stability of gravity solitary waves in the presence of weak surface tension. Topol. Methods Nonlinear Anal. 2005, 25:41-68.
    • (2005) Topol. Methods Nonlinear Anal. , vol.25 , pp. 41-68
    • Buffoni, B.1
  • 11
    • 0000090159 scopus 로고
    • Orbital stability of standing waves for some nonlinear Schrödinger equations
    • Cazenave T., Lions P.L. Orbital stability of standing waves for some nonlinear Schrödinger equations. Comm. Math. Phys. 1982, 85:549-561.
    • (1982) Comm. Math. Phys. , vol.85 , pp. 549-561
    • Cazenave, T.1    Lions, P.L.2
  • 12
    • 30444438571 scopus 로고
    • Water waves, Hamiltonian systems and Cauchy integrals
    • Springer-Verlag, New York, M. Beals, R.B. Melrose, J. Rauch (Eds.)
    • Craig W. Water waves, Hamiltonian systems and Cauchy integrals. Microlocal Analysis and Nonlinear Waves 1991, 37-45. Springer-Verlag, New York. M. Beals, R.B. Melrose, J. Rauch (Eds.).
    • (1991) Microlocal Analysis and Nonlinear Waves , pp. 37-45
    • Craig, W.1
  • 13
    • 0034550889 scopus 로고    scopus 로고
    • Traveling two and three dimensional capillary gravity water waves
    • Craig W., Nicholls D.P. Traveling two and three dimensional capillary gravity water waves. SIAM J. Math. Anal. 2000, 32:323-359.
    • (2000) SIAM J. Math. Anal. , vol.32 , pp. 323-359
    • Craig, W.1    Nicholls, D.P.2
  • 14
    • 0002267149 scopus 로고    scopus 로고
    • Remarks on the stability of generalized KP solitary waves
    • de Bouard A., Saut J.-C. Remarks on the stability of generalized KP solitary waves. Contemp. Math. 1996, vol. 200:75-84.
    • (1996) Contemp. Math. , vol.200 , pp. 75-84
    • de Bouard, A.1    Saut, J.-C.2
  • 16
    • 84857870242 scopus 로고    scopus 로고
    • Global solutions for the gravity water waves equation in dimension 3
    • Germain P., Masmoudi N., Shatah J. Global solutions for the gravity water waves equation in dimension 3. Ann. of Math. 2012, 175:691-754.
    • (2012) Ann. of Math. , vol.175 , pp. 691-754
    • Germain, P.1    Masmoudi, N.2    Shatah, J.3
  • 17
    • 84867952271 scopus 로고    scopus 로고
    • A bifurcation theory for three-dimensional oblique travelling gravity-capillary water waves
    • Groves M.D., Haragus M. A bifurcation theory for three-dimensional oblique travelling gravity-capillary water waves. J. Nonlinear Sci. 2003, 13:397-447.
    • (2003) J. Nonlinear Sci. , vol.13 , pp. 397-447
    • Groves, M.D.1    Haragus, M.2
  • 18
    • 43149083695 scopus 로고    scopus 로고
    • Fully localised solitary-wave solutions of the three-dimensional gravity-capillary water-wave problem
    • Groves M.D., Sun S.-M. Fully localised solitary-wave solutions of the three-dimensional gravity-capillary water-wave problem. Arch. Ration. Mech. Anal. 2008, 188:1-91.
    • (2008) Arch. Ration. Mech. Anal. , vol.188 , pp. 1-91
    • Groves, M.D.1    Sun, S.-M.2
  • 20
    • 85030707196 scopus 로고
    • The concentration-compactness principle in the calculus of variations. The locally compact case, part 1
    • Lions P.L. The concentration-compactness principle in the calculus of variations. The locally compact case, part 1. Ann. Inst. H. Poincaré Anal. Non Linéaire 1984, 1:109-145.
    • (1984) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.1 , pp. 109-145
    • Lions, P.L.1
  • 21
    • 85030719142 scopus 로고
    • The concentration-compactness principle in the calculus of variations. The locally compact case, part 2
    • Lions P.L. The concentration-compactness principle in the calculus of variations. The locally compact case, part 2. Ann. Inst. H. Poincaré Anal. Non Linéaire 1984, 1:223-283.
    • (1984) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.1 , pp. 223-283
    • Lions, P.L.1
  • 22
    • 0031539724 scopus 로고    scopus 로고
    • Nonlinear stability of solitary waves of a generalised Kadomtsev-Petviashvili equation
    • Liu Y., Wang X.P. Nonlinear stability of solitary waves of a generalised Kadomtsev-Petviashvili equation. Comm. Math. Phys. 1997, 183:253-266.
    • (1997) Comm. Math. Phys. , vol.183 , pp. 253-266
    • Liu, Y.1    Wang, X.P.2
  • 24
    • 0037107586 scopus 로고    scopus 로고
    • On the energetic stability of solitary water waves
    • Mielke A. On the energetic stability of solitary water waves. Philos. Trans. R. Soc. Lond. Ser. A 2002, 360:2337-2358.
    • (2002) Philos. Trans. R. Soc. Lond. Ser. A , vol.360 , pp. 2337-2358
    • Mielke, A.1
  • 25
    • 84859700774 scopus 로고    scopus 로고
    • Large time well-posedness of the three-dimensional capillary-gravity waves in the long wave regime
    • Ming M., Zhang P., Zhang Z. Large time well-posedness of the three-dimensional capillary-gravity waves in the long wave regime. Arch. Ration. Mech. Anal. 2012, 204:387-444.
    • (2012) Arch. Ration. Mech. Anal. , vol.204 , pp. 387-444
    • Ming, M.1    Zhang, P.2    Zhang, Z.3
  • 26
    • 23044528812 scopus 로고    scopus 로고
    • A new approach to analyticity of Dirichlet-Neumann operators
    • Nicholls D.P., Reitich F. A new approach to analyticity of Dirichlet-Neumann operators. Proc. Roy. Soc. Edinburgh Sect. A 2001, 131:1411-1433.
    • (2001) Proc. Roy. Soc. Edinburgh Sect. A , vol.131 , pp. 1411-1433
    • Nicholls, D.P.1    Reitich, F.2
  • 27
    • 27844570258 scopus 로고    scopus 로고
    • On ground-traveling waves for the generalized Kadomtsev-Petviashvili equations
    • Pankov A., Pflüger K. On ground-traveling waves for the generalized Kadomtsev-Petviashvili equations. Math. Phys. Anal. Geom. 2000, 3:33-47.
    • (2000) Math. Phys. Anal. Geom. , vol.3 , pp. 33-47
    • Pankov, A.1    Pflüger, K.2
  • 28
    • 31144445710 scopus 로고    scopus 로고
    • Three-dimensional gravity-capillary solitary waves in water of finite depth and related problems
    • Parau E.I., Vanden-Broeck J.-M., Cooker M.J. Three-dimensional gravity-capillary solitary waves in water of finite depth and related problems. Phys. Fluids 2005, 17:122101.
    • (2005) Phys. Fluids , vol.17 , pp. 122101
    • Parau, E.I.1    Vanden-Broeck, J.-M.2    Cooker, M.J.3
  • 29
    • 0001108712 scopus 로고    scopus 로고
    • Two-dimensional solitary waves for a Benny-Luke equation
    • Pego R.L., Quintero J.R. Two-dimensional solitary waves for a Benny-Luke equation. Phys. D 1999, 132:476-496.
    • (1999) Phys. D , vol.132 , pp. 476-496
    • Pego, R.L.1    Quintero, J.R.2
  • 31
    • 39449131486 scopus 로고    scopus 로고
    • A multiplicity result for the generalized Kadomtsev-Petviashvili equation
    • Wang Z.Q., Willem M. A multiplicity result for the generalized Kadomtsev-Petviashvili equation. Topol. Methods Nonlinear Anal. 1996, 7:261-270.
    • (1996) Topol. Methods Nonlinear Anal. , vol.7 , pp. 261-270
    • Wang, Z.Q.1    Willem, M.2
  • 32
    • 67650433790 scopus 로고    scopus 로고
    • Almost global wellposedness of the 2-D full water wave problem
    • Wu S. Almost global wellposedness of the 2-D full water wave problem. Invent. Math. 2009, 177:45-135.
    • (2009) Invent. Math. , vol.177 , pp. 45-135
    • Wu, S.1
  • 33
    • 79952989811 scopus 로고    scopus 로고
    • Global wellposedness of the 3-D full water wave problem
    • Wu S. Global wellposedness of the 3-D full water wave problem. Invent. Math. 2011, 184:125-220.
    • (2011) Invent. Math. , vol.184 , pp. 125-220
    • Wu, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.