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Volumn 208, Issue 2, 2013, Pages 481-567

A Stability Criterion for Two-Fluid Interfaces and Applications

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EID: 84875533999     PISSN: 00039527     EISSN: 14320673     Source Type: Journal    
DOI: 10.1007/s00205-012-0604-6     Document Type: Article
Times cited : (70)

References (68)
  • 1
    • 79959880152 scopus 로고    scopus 로고
    • On the Cauchy problem for the water waves with surface tension
    • Alazard T., Burq N., Zuily C.: On the Cauchy problem for the water waves with surface tension. Duke Math. J. 158, 413-499 (2011).
    • (2011) Duke Math. J. , vol.158 , pp. 413-499
    • Alazard, T.1    Burq, N.2    Zuily, C.3
  • 3
    • 74949116792 scopus 로고    scopus 로고
    • Paralinearization of the Dirichlet to Neumann operator, and regularity of three-dimensional water waves
    • Alazard T., Métivier G.: Paralinearization of the Dirichlet to Neumann operator, and regularity of three-dimensional water waves. Commun. Partial Differ. Equ. 34, 1632-1704 (2009).
    • (2009) Commun. Partial Differ. Equ. , vol.34 , pp. 1632-1704
    • Alazard, T.1    Métivier, G.2
  • 4
    • 38349102793 scopus 로고    scopus 로고
    • Large time existence for 3d water-waves and asymptotics
    • Alvarez-Samaniego B., Lannes D.: Large time existence for 3d water-waves and asymptotics. Invent. Math. 171, 485-541 (2008).
    • (2008) Invent. Math. , vol.171 , pp. 485-541
    • Alvarez-Samaniego, B.1    Lannes, D.2
  • 5
    • 1342266714 scopus 로고    scopus 로고
    • Well-posedness of vortex sheets with surface tension
    • Ambrose D.: Well-posedness of vortex sheets with surface tension. SIAM J. Math. Anal. 35, 211-244 (2003).
    • (2003) SIAM J. Math. Anal. , vol.35 , pp. 211-244
    • Ambrose, D.1
  • 6
    • 26944460000 scopus 로고    scopus 로고
    • The zero surface tension limit of two-dimensional water waves
    • Ambrose D. M., Masmoudi N.: The zero surface tension limit of two-dimensional water waves. Commun. Pure Appl. Math. 58, 1287-1315 (2005).
    • (2005) Commun. Pure Appl. Math. , vol.58 , pp. 1287-1315
    • Ambrose, D.M.1    Masmoudi, N.2
  • 7
    • 67249144683 scopus 로고    scopus 로고
    • The zero surface tension limit of three-dimensional water waves
    • Ambrose D. M., Masmoudi N.: The zero surface tension limit of three-dimensional water waves. Indiana Univ. Math. J. 58, 479-521 (2009).
    • (2009) Indiana Univ. Math. J. , vol.58 , pp. 479-521
    • Ambrose, D.M.1    Masmoudi, N.2
  • 8
    • 34547194744 scopus 로고    scopus 로고
    • Well-posedness of 3D vortex sheets with surface tension
    • Ambrose D., Masmoudi N.: Well-posedness of 3D vortex sheets with surface tension. Commun. Math. Sci. 5, 391-430 (2007).
    • (2007) Commun. Math. Sci. , vol.5 , pp. 391-430
    • Ambrose, D.1    Masmoudi, N.2
  • 10
    • 0031079899 scopus 로고    scopus 로고
    • Reappraisal of the KelvinHelmholtz problem. Part 1. Hamiltonian structure
    • Benjamin T. B., Bridges T. J.: Reappraisal of the KelvinHelmholtz problem. Part 1. Hamiltonian structure. J. Fluid Mech. 333, 301-325 (1997).
    • (1997) J. Fluid Mech. , vol.333 , pp. 301-325
    • Benjamin, T.B.1    Bridges, T.J.2
  • 14
    • 55749106935 scopus 로고    scopus 로고
    • On the motion of Vortex Sheets with surface tension
    • Cheng A., Coutand D., Shkoller S.: On the motion of Vortex Sheets with surface tension. Commun. Pure Appl. Math. 61, 1715-1752 (2008).
    • (2008) Commun. Pure Appl. Math. , vol.61 , pp. 1715-1752
    • Cheng, A.1    Coutand, D.2    Shkoller, S.3
  • 15
    • 77950959732 scopus 로고    scopus 로고
    • On the limit as the density ratio tends to zero for two perfect incompressible 3-D fluids separated by a surface of discontinuity
    • Cheng A., Coutand D., Shkoller S.: On the limit as the density ratio tends to zero for two perfect incompressible 3-D fluids separated by a surface of discontinuity. Commun. Partial Differ. Equ. 35, 817-845 (2010).
    • (2010) Commun. Partial Differ. Equ. , vol.35 , pp. 817-845
    • Cheng, A.1    Coutand, D.2    Shkoller, S.3
  • 16
    • 0002988577 scopus 로고    scopus 로고
    • Fully nonlinear internal waves in a two-fluid system
    • Choi W., Camassa R.: Fully nonlinear internal waves in a two-fluid system. J. Fluid Mech. 396, 1-36 (1999).
    • (1999) J. Fluid Mech. , vol.396 , pp. 1-36
    • Choi, W.1    Camassa, R.2
  • 17
    • 78049501969 scopus 로고    scopus 로고
    • Strichartz estimates for the water-wave problem with surface tension
    • Christianson H., Hur V. M., Staffilani G.: Strichartz estimates for the water-wave problem with surface tension. Commun. Partial Differ. Equ. 35, 2195-2252 (2010).
    • (2010) Commun. Partial Differ. Equ. , vol.35 , pp. 2195-2252
    • Christianson, H.1    Hur, V.M.2    Staffilani, G.3
  • 18
    • 70350325132 scopus 로고    scopus 로고
    • Interface evolution: water waves in 2 - D
    • Cordoba A., Cordoba D., Gancedo F.: Interface evolution: water waves in 2 - D. Adv. Math. 223, 120-173 (2010).
    • (2010) Adv. Math. , vol.223 , pp. 120-173
    • Cordoba, A.1    Cordoba, D.2    Gancedo, F.3
  • 19
    • 34548446988 scopus 로고    scopus 로고
    • Well-posedness of the free-surface incompressible Euler equations with or without surface tension
    • Coutand D., Shkoller S.: Well-posedness of the free-surface incompressible Euler equations with or without surface tension. J. Am. Math. Soc. 20, 829-930 (2007).
    • (2007) J. Am. Math. Soc. , vol.20 , pp. 829-930
    • Coutand, D.1    Shkoller, S.2
  • 20
    • 0001688084 scopus 로고
    • An existence theory for water waves and the Boussinesq and Korteweg-de Vries scaling limits
    • Craig W.: An existence theory for water waves and the Boussinesq and Korteweg-de Vries scaling limits. Commun. Partial Differ. Equ. 10, 787-1003 (1985).
    • (1985) Commun. Partial Differ. Equ. , vol.10 , pp. 787-1003
    • Craig, W.1
  • 21
    • 30544433668 scopus 로고    scopus 로고
    • Hamiltonian long-wave expansions for free surfaces and interfaces
    • Craig W., Guyenne P., Kalisch H.: Hamiltonian long-wave expansions for free surfaces and interfaces. Commun. Pure Appl. Math. 58, 1587-1641 (2005).
    • (2005) Commun. Pure Appl. Math. , vol.58 , pp. 1587-1641
    • Craig, W.1    Guyenne, P.2    Kalisch, H.3
  • 22
    • 0002686768 scopus 로고
    • Numerical simulation of gravity waves
    • Craig W., Sulem C.: Numerical simulation of gravity waves. J. Comput. Phys. 108, 73-83 (1993).
    • (1993) J. Comput. Phys. , vol.108 , pp. 73-83
    • Craig, W.1    Sulem, C.2
  • 24
    • 0344453090 scopus 로고
    • Ill-posedness of the Rayleigh-Taylor and Kelvin-Helmotz problems for incompressible fluids
    • Ebin G.: Ill-posedness of the Rayleigh-Taylor and Kelvin-Helmotz problems for incompressible fluids. Commun. Partial Differ. Equ. 13, 1265-1295 (1988).
    • (1988) Commun. Partial Differ. Equ. , vol.13 , pp. 1265-1295
    • Ebin, G.1
  • 25
    • 4344709446 scopus 로고    scopus 로고
    • Transmission problems and spectral theory for singular integral operators on Lipschitz domains
    • Escauriaza L., Mitrea M.: Transmission problems and spectral theory for singular integral operators on Lipschitz domains. J. Funct. Anal. 216, 141-171 (2004).
    • (2004) J. Funct. Anal. , vol.216 , pp. 141-171
    • Escauriaza, L.1    Mitrea, M.2
  • 26
    • 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. Math. 175, 691-754 (2012).
    • (2012) Ann. Math. , vol.175 , pp. 691-754
    • Germain, P.1    Masmoudi, N.2    Shatah, J.3
  • 27
    • 0031503817 scopus 로고    scopus 로고
    • Pseudo-differential energy estimates of singular perturbations
    • Grenier E.: Pseudo-differential energy estimates of singular perturbations. Commun. Pure Appl. Math. 50, 821-865 (1997).
    • (1997) Commun. Pure Appl. Math. , vol.50 , pp. 821-865
    • Grenier, E.1
  • 29
    • 74849088012 scopus 로고    scopus 로고
    • Well-posedness of the Cauchy problem for models of large amplitude internal waves
    • Guyenne P., Lannes D., Saut J.-C.: Well-posedness of the Cauchy problem for models of large amplitude internal waves. Nonlinearity 23, 237-275 (2010).
    • (2010) Nonlinearity , vol.23 , pp. 237-275
    • Guyenne, P.1    Lannes, D.2    Saut, J.-C.3
  • 31
    • 0038473867 scopus 로고    scopus 로고
    • A nearly optimal existence result for slightly perturbed 3-D vortex sheets
    • Hou T. Y., Hu G.: A nearly optimal existence result for slightly perturbed 3-D vortex sheets. Commun. Partial Differ. Equ. 28, 155-198 (2003).
    • (2003) Commun. Partial Differ. Equ. , vol.28 , pp. 155-198
    • Hou, T.Y.1    Hu, G.2
  • 32
    • 33847163682 scopus 로고    scopus 로고
    • A long wave approximation for capillary-gravity waves and an effect of the bottom
    • Iguchi T.: A long wave approximation for capillary-gravity waves and an effect of the bottom. Commun. Partial Differ. Equ. 32, 37-85 (2007).
    • (2007) Commun. Partial Differ. Equ. , vol.32 , pp. 37-85
    • Iguchi, T.1
  • 33
    • 77950220771 scopus 로고    scopus 로고
    • A long wave approximation for capillary-gravity waves and the Kawahara equation
    • Iguchi T.: A long wave approximation for capillary-gravity waves and the Kawahara equation. Bull. Inst. Math. Acad. Sin. (N. S.) 2, 179-220 (2007).
    • (2007) Bull. Inst. Math. Acad. Sin. (N.S.) , vol.2 , pp. 179-220
    • Iguchi, T.1
  • 34
    • 69549128379 scopus 로고    scopus 로고
    • A shallow water approximation for water waves
    • Iguchi T.: A shallow water approximation for water waves. J. Math. Kyoto Univ. 49, 13-55 (2009).
    • (2009) J. Math. Kyoto Univ. , vol.49 , pp. 13-55
    • Iguchi, T.1
  • 35
    • 0031522531 scopus 로고    scopus 로고
    • On the two-phase free boundary problem for two-dimensional water waves
    • Iguchi T., Tanaka N., Tani A.: On the two-phase free boundary problem for two-dimensional water waves. Math. Ann. 309, 199-223 (1997).
    • (1997) Math. Ann. , vol.309 , pp. 199-223
    • Iguchi, T.1    Tanaka, N.2    Tani, A.3
  • 36
    • 17044418131 scopus 로고    scopus 로고
    • On 2D Rayleigh-Taylor instabilities
    • Kamotski V., Lebeau G.: On 2D Rayleigh-Taylor instabilities. Asymptot. Anal. 42, 1-27 (2005).
    • (2005) Asymptot. Anal. , vol.42 , pp. 1-27
    • Kamotski, V.1    Lebeau, G.2
  • 37
    • 0019633062 scopus 로고
    • An investigation of internal solitary waves in a two-fluid system
    • Koop C. G., Butler G.: An investigation of internal solitary waves in a two-fluid system. J. Fluid Mech. 112, 225-251 (1981).
    • (1981) J. Fluid Mech. , vol.112 , pp. 225-251
    • Koop, C.G.1    Butler, G.2
  • 38
    • 11744344543 scopus 로고
    • Nonlinear theory of the excitation of waves by a wind due to the Kelvin-Helmholtz instability
    • Kuznetsov E. A., Lushnikov P. L.: Nonlinear theory of the excitation of waves by a wind due to the Kelvin-Helmholtz instability. JETP 81, 332-340 (1995).
    • (1995) Jetp , vol.81 , pp. 332-340
    • Kuznetsov, E.A.1    Lushnikov, P.L.2
  • 39
    • 22544482964 scopus 로고    scopus 로고
    • Well-posedness of the water-waves equations
    • Lannes D.: Well-posedness of the water-waves equations. J. Am. Math. Soc. 18, 605-654 (2005).
    • (2005) J. Am. Math. Soc. , vol.18 , pp. 605-654
    • Lannes, D.1
  • 40
    • 31744440292 scopus 로고    scopus 로고
    • Sharp estimates for pseudo-differential operators with symbols of limited smoothness and commutators
    • Lannes D.: Sharp estimates for pseudo-differential operators with symbols of limited smoothness and commutators. J. Funct. Anal. 232, 495-539 (2006).
    • (2006) J. Funct. Anal. , vol.232 , pp. 495-539
    • Lannes, D.1
  • 41
    • 84899790304 scopus 로고    scopus 로고
    • The water waves problem: mathematical analysis and asymptotics
    • AMS (in press)
    • Lannes, D.: The water waves problem: mathematical analysis and asymptotics. Mathematical Surveys and Monographs. AMS (in press).
    • Mathematical Surveys and Monographs
    • Lannes, D.1
  • 42
    • 17044425556 scopus 로고    scopus 로고
    • Régularité du problème de Kelvin-Helmholtz pour l'équation d'Euler 2d
    • Lebeau G.: Régularité du problème de Kelvin-Helmholtz pour l'équation d'Euler 2d. ESAIM: COCV 08(801-825), 08, 801-825 (2002).
    • (2002) ESAIM: COCV , vol.8 , Issue.801-825 , pp. 801-825
    • Lebeau, G.1
  • 43
    • 26044448758 scopus 로고    scopus 로고
    • Well-posedness for the motion of an incompressible liquid with free surface boundary
    • Lindblad, H.: Well-posedness for the motion of an incompressible liquid with free surface boundary. Ann. Math. (2)162, 109-194 (2005).
    • (2005) Ann. Math. , vol.162 , Issue.2 , pp. 109-194
    • Lindblad, H.1
  • 44
    • 71549133352 scopus 로고    scopus 로고
    • Well-posedness of the water-wave problem with surface tension
    • Ming M., Zhang Z.: Well-posedness of the water-wave problem with surface tension. J. Math. Pures Appl. 92, 429-455 (2009).
    • (2009) J. Math. Pures Appl. , vol.92 , pp. 429-455
    • Ming, M.1    Zhang, Z.2
  • 45
    • 0000306561 scopus 로고
    • The Cauchy-Poisson problem (Russian), Dinamika Splosn. Sredy Vyp. 18 Dinamika Zidkost. so Svobod
    • Nalimov, V. I.: The Cauchy-Poisson problem (Russian), Dinamika Splosn. Sredy Vyp. 18 Dinamika Zidkost. so Svobod. Granicami 254, 104-210 (1974).
    • (1974) Granicami , vol.254 , pp. 104-210
    • Nalimov, V.I.1
  • 46
    • 48349100318 scopus 로고    scopus 로고
    • A Boussinesq system for two-way propagation of interfacial waves
    • Nguyen H. Y., Dias F.: A Boussinesq system for two-way propagation of interfacial waves. Physica D 237, 2365-2389 (2008).
    • (2008) Physica D , vol.237 , pp. 2365-2389
    • Nguyen, H.Y.1    Dias, F.2
  • 47
    • 62649143819 scopus 로고    scopus 로고
    • A two-phase problem for capillary-gravity waves and the Benjamin-Ono equation. Discrete Contin
    • Ohi K., Iguchi T.: A two-phase problem for capillary-gravity waves and the Benjamin-Ono equation. Discrete Contin. Dyn. Syst. 23, 1205-1240 (2009).
    • (2009) Dyn. Syst. , vol.23 , pp. 1205-1240
    • Ohi, K.1    Iguchi, T.2
  • 48
    • 0039742211 scopus 로고
    • Cauchy problem in a scale of Banach spaces and its application to the shallow water theory justification
    • (Joint Sympos., IUTAM/IMU, Marseille, 1975)
    • Ovsjannikov, L. V.: Cauchy problem in a scale of Banach spaces and its application to the shallow water theory justification. In: Applications of Methods of Functional Analysis to Problems in Mechanics (Joint Sympos., IUTAM/IMU, Marseille, 1975), pp. 426-437. Lecture Notes in Mathematics, vol. 503. Springer, Berlin, 1976.
    • (1976) Applications of Methods of Functional Analysis to Problems in Mechanics , vol.503 , pp. 426-437
    • Ovsjannikov, L.V.1
  • 50
    • 79959970992 scopus 로고    scopus 로고
    • On the limit as the surface tension and density ratio tend to zero for the twophase Euler equations
    • Pusateri F.: On the limit as the surface tension and density ratio tend to zero for the twophase Euler equations. J. Hyperb. Differ. Equ. 8, 347-373 (2011).
    • (2011) J. Hyperb. Differ. Equ. , vol.8 , pp. 347-373
    • Pusateri, F.1
  • 51
    • 79954988210 scopus 로고    scopus 로고
    • Transverse instability of the line solitary water-waves
    • Rousset F., Tzvetkov N.: Transverse instability of the line solitary water-waves. Invent. Math. 184, 257-388 (2011).
    • (2011) Invent. Math. , vol.184 , pp. 257-388
    • Rousset, F.1    Tzvetkov, N.2
  • 52
    • 77953866714 scopus 로고    scopus 로고
    • On the transverse instability of one dimensional capillary-gravity waves
    • Rousset F., Tzvetkov N.: On the transverse instability of one dimensional capillary-gravity waves. DCDS-B 13, 859-872 (2010).
    • (2010) Dcds-B , vol.13 , pp. 859-872
    • Rousset, F.1    Tzvetkov, N.2
  • 53
    • 0036012969 scopus 로고    scopus 로고
    • The rigorous approximation of long-wavelength capillary-gravity waves
    • Schneider G., Wayne C. E.: The rigorous approximation of long-wavelength capillary-gravity waves. Arch. Ration. Mech. Anal. 162, 247-285 (2002).
    • (2002) Arch. Ration. Mech. Anal. , vol.162 , pp. 247-285
    • Schneider, G.1    Wayne, C.E.2
  • 54
    • 52349104032 scopus 로고    scopus 로고
    • Geometry and a priori estimates for free boundary problems of the Euler equation
    • Shatah J., Zeng C.: Geometry and a priori estimates for free boundary problems of the Euler equation. Commun. Pure Appl. Math. 61, 698-744 (2008).
    • (2008) Commun. Pure Appl. Math. , vol.61 , pp. 698-744
    • Shatah, J.1    Zeng, C.2
  • 55
    • 52349092767 scopus 로고    scopus 로고
    • A priori estimates for fluid interface problems
    • Shatah J., Zeng C.: A priori estimates for fluid interface problems. Commun. Pure Appl. Math. 61, 848-876 (2008).
    • (2008) Commun. Pure Appl. Math. , vol.61 , pp. 848-876
    • Shatah, J.1    Zeng, C.2
  • 56
    • 78751704957 scopus 로고    scopus 로고
    • Local well-posedness for fluid interface problems
    • Shatah J., Zeng C.: Local well-posedness for fluid interface problems. Arch. Ration. Mech. Anal. 199, 653-705 (2011).
    • (2011) Arch. Ration. Mech. Anal. , vol.199 , pp. 653-705
    • Shatah, J.1    Zeng, C.2
  • 57
    • 0004121498 scopus 로고    scopus 로고
    • Partial Differential Equations II: Qualitative Studies of Linear Equations
    • Springer, Berlin
    • Taylor, M. E.: Partial Differential Equations II: Qualitative Studies of Linear Equations. Applied Mathematical Sciences, vol. 116. Springer, Berlin, 1996.
    • (1996) Applied Mathematical Sciences , vol.116
    • Taylor, M.E.1
  • 58
    • 0003278083 scopus 로고    scopus 로고
    • Partial Differential Equations III
    • Springer, New York, Nonlinear Equations. Corrected reprint of the 1996 original
    • Taylor, M. E.: Partial Differential Equations III. Applied Mathematical Sciences, vol. 117. Springer, New York, 1997. Nonlinear Equations. Corrected reprint of the 1996 original.
    • (1997) Applied Mathematical Sciences , vol.117
    • Taylor, M.E.1
  • 59
    • 84968512992 scopus 로고
    • Finite time analyticity for the two- and three-dimensional Rayleigh-Taylor instability
    • Sulem C., Sulem P.-L.: Finite time analyticity for the two- and three-dimensional Rayleigh-Taylor instability. Trans. Am. Math. Soc. 287, 127-160 (1981).
    • (1981) Trans. Am. Math. Soc. , vol.287 , pp. 127-160
    • Sulem, C.1    Sulem, P.-L.2
  • 60
    • 0038247451 scopus 로고
    • Finite time analyticity for the two- and three-dimensional Kelvin-Helmholtz instability
    • Sulem C., Sulem P.-L., Bardos C., Frisch U.: Finite time analyticity for the two- and three-dimensional Kelvin-Helmholtz instability. Commun. Math. Phys. 80, 485-516 (1981).
    • (1981) Commun. Math. Phys. , vol.80 , pp. 485-516
    • Sulem, C.1    Sulem, P.-L.2    Bardos, C.3    Frisch, U.4
  • 61
    • 85045585725 scopus 로고    scopus 로고
    • Well-posedeness in Sobolev spaces of the full water wave problem in 2-D
    • Wu S.: Well-posedeness in Sobolev spaces of the full water wave problem in 2-D. Invent. Math. 130, 439-472 (1997).
    • (1997) Invent. Math. , vol.130 , pp. 439-472
    • Wu, S.1
  • 62
    • 0033446356 scopus 로고    scopus 로고
    • Well-posedness in Sobolev spaces of the full water wave problem in 3-D
    • Wu S.: Well-posedness in Sobolev spaces of the full water wave problem in 3-D. J. Am. Math. Soc. 12, 445-495 (1999).
    • (1999) J. Am. Math. Soc. , vol.12 , pp. 445-495
    • Wu, S.1
  • 63
    • 33745626744 scopus 로고    scopus 로고
    • Mathematical analysis of vortex sheets
    • Wu S.: Mathematical analysis of vortex sheets. Commun. Pure Appl. Math. 59, 1065-1206 (2006).
    • (2006) Commun. Pure Appl. Math. , vol.59 , pp. 1065-1206
    • Wu, S.1
  • 64
    • 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. 177, 45-135 (2009).
    • (2009) Invent. Math. , vol.177 , pp. 45-135
    • Wu, S.1
  • 65
    • 79952989811 scopus 로고    scopus 로고
    • Global well-posedness of the 3-D full water wave problem
    • Wu S.: Global well-posedness of the 3-D full water wave problem. Invent. Math. 184, 125-220 (2011).
    • (2011) Invent. Math. , vol.184 , pp. 125-220
    • Wu, S.1
  • 66
    • 85009585833 scopus 로고
    • Gravity waves on the free surface of an incompressible perfect fluid of finite depth
    • Yosihara H.: Gravity waves on the free surface of an incompressible perfect fluid of finite depth. Publ. Res. Inst. Math. Sci. 18, 49-96 (1982).
    • (1982) Publ. Res. Inst. Math. Sci. , vol.18 , pp. 49-96
    • Yosihara, H.1
  • 67
    • 0000375767 scopus 로고
    • Capillary-gravity waves for an incompressible ideal fluid
    • Yosihara H.: Capillary-gravity waves for an incompressible ideal fluid. J. Math. Kyoto Univ. 23, 649-694 (1983).
    • (1983) J. Math. Kyoto Univ. , vol.23 , pp. 649-694
    • Yosihara, H.1
  • 68
    • 34250447917 scopus 로고
    • Stability of periodic waves of nite amplitude on the surface of a deep fluid
    • Zakharov V. E.: Stability of periodic waves of nite amplitude on the surface of a deep fluid. J. Appl. Mech. Tech. Phys. 9, 190-194 (1968).
    • (1968) J. Appl. Mech. Tech. Phys. , vol.9 , pp. 190-194
    • Zakharov, V.E.1


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