A Riemann-Hilbert problem and the Bernoulli boundary condition in the variational theory of Stokes waves
Annales de l'I.H.P. Analyse non linéaire, Volume 20 (2003) no. 1, p. 37-52
@article{AIHPC_2003__20_1_37_0,
     author = {Shargorodsky, E. and Toland, J. F.},
     title = {A Riemann-Hilbert problem and the Bernoulli boundary condition in the variational theory of Stokes waves},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {20},
     number = {1},
     year = {2003},
     pages = {37-52},
     mrnumber = {1958161},
     zbl = {1045.35113},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2003__20_1_37_0}
}
Shargorodsky, E.; Toland, J. F. A Riemann-Hilbert problem and the Bernoulli boundary condition in the variational theory of Stokes waves. Annales de l'I.H.P. Analyse non linéaire, Volume 20 (2003) no. 1, pp. 37-52. http://www.numdam.org/item/AIHPC_2003__20_1_37_0/

[1] Babenko K.I., Some remarks on the theory of surface waves of finite amplitude, Soviet Math. Dokl. 35 (3) (1987) 599-603, See also loc. cit. 647-650. | MR 898306 | Zbl 0641.76007

[2] Buffoni B., Dancer E.N., Toland J.F., The regularity and local bifurcation of Stokes waves, Arch. Rational Mech. Anal. 152 (3) (2000) 207-240. | MR 1764945 | Zbl 0959.76010

[3] Buffoni B., Dancer E.N., Toland J.F., The sub-harmonic bifurcation of Stokes waves, Arch. Rational Mech. Anal. 152 (3) (2000) 241-270. | MR 1764946 | Zbl 0962.76012

[4] Dyachenko A.I., Kuznetsov E.A., Spector M.D., Zakharov V.E., Analytic description of the free surface dynamics of an ideal fluid (canonical formalism and conformal mapping), Phys. Lett. A 1 (1996) 73-79.

[5] Gakhov F.D., Boundary Value Problems, Pergamon Press, Oxford, 1966. | MR 198152 | Zbl 0141.08001

[6] Garnett J.B., Bounded Analytic Functions, Academic Press, New York, 1981. | MR 628971 | Zbl 0469.30024

[7] Koosis P., Introduction to Hp Spaces, Cambridge University Press, Cambridge, 1999. | MR 1669574 | Zbl 1024.30001

[8] Lewy H., A note on harmonic functions and a hydrodynamic application, Proc. Amer. Math. Soc. 3 (1952) 111-113. | MR 49399 | Zbl 0046.41706

[9] Lieb E.H., Loss M., Analysis, Graduate Studies in Mathematics, 14, American Mathematical Society, Providence, RI, 1997. | MR 1415616 | Zbl 0873.26002

[10] Mcleod J.B., The Stokes and Krasovskii conjectures for the wave of greatest height, in: Studies in Applied Math., 98, 1997, pp. 311-334, In pre-print-form: Univ. of Wisconsin Mathematics Research Center Report Number 2041, 1979 (sic). | MR 1446239 | Zbl 0882.76014

[11] Muskhelishvili N.I., Singular Integral Equations, Wolters-Noordhoff Publishing, Groningen, 1972. | MR 355494 | Zbl 0174.16201

[12] Plotnikov P.I., Non-uniqueness of solutions of the problem of solitary waves and bifurcation of critical points of smooth functionals, Math. USSR Izvestiya 38 (2) (1992) 333-357. | Zbl 0795.76017

[13] Rudin W., Real and Complex Analysis, McGraw-Hill, New York, 1986. | Zbl 0925.00005

[14] Toland J.F., Stokes waves, Topological Methods in Nonlinear Analysis 7 (1996) 1-48, Topological Methods in Nonlinear Analysis 8 (1997) 412-414. | MR 1422004 | Zbl 0897.35067

[15] Toland J.F., Regularity of Stokes waves in Hardy spaces and in spaces of distributions, J. Math. Pure Appl. 79 (9) (2000) 901-917. | MR 1792729 | Zbl 0976.35052

[16] Toland J.F., On a pseudo-differential equation for Stokes waves, Arch. Rational Mech. Anal. 162 (2002) 179-189. | MR 1897380 | Zbl 1028.35126

[17] Torchinsky A., Real-Variable Methods in Harmonic Analysis, Academic Press, Orlando, 1986. | MR 869816 | Zbl 0621.42001

[18] Zygmund A., Trigonometric Series I & II, Cambridge University Press, Cambridge, 1959. | MR 107776 | Zbl 0367.42001