A Riemann–Hilbert problem and the Bernoulli boundary condition in the variational theory of Stokes waves

E. Shargorodsky; J. F. Toland

Annales de l'I.H.P. Analyse non linéaire (2003)

  • Volume: 20, Issue: 1, page 37-52
  • ISSN: 0294-1449

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Shargorodsky, E., and 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 20.1 (2003): 37-52. <http://eudml.org/doc/78573>.

@article{Shargorodsky2003,
author = {Shargorodsky, E., Toland, J. F.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {regularity theory; Stokes waves; critical point; Bernoulli boundary condition; Euler-Lagrange equation},
language = {eng},
number = {1},
pages = {37-52},
publisher = {Elsevier},
title = {A Riemann–Hilbert problem and the Bernoulli boundary condition in the variational theory of Stokes waves},
url = {http://eudml.org/doc/78573},
volume = {20},
year = {2003},
}

TY - JOUR
AU - Shargorodsky, E.
AU - Toland, J. F.
TI - A Riemann–Hilbert problem and the Bernoulli boundary condition in the variational theory of Stokes waves
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2003
PB - Elsevier
VL - 20
IS - 1
SP - 37
EP - 52
LA - eng
KW - regularity theory; Stokes waves; critical point; Bernoulli boundary condition; Euler-Lagrange equation
UR - http://eudml.org/doc/78573
ER -

References

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  2. [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. Zbl0959.76010MR1764945
  3. [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. Zbl0962.76012MR1764946
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  10. [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). Zbl0882.76014MR1446239
  11. [11] Muskhelishvili N.I., Singular Integral Equations, Wolters–Noordhoff Publishing, Groningen, 1972. Zbl0174.16201MR355494
  12. [12] Plotnikov P.I., Non-uniqueness of solutions of the problem of solitary waves and bifurcation of critical points of smooth functionals, Math. USSR Izvestiya38 (2) (1992) 333-357. Zbl0795.76017
  13. [13] Rudin W., Real and Complex Analysis, McGraw-Hill, New York, 1986. Zbl0925.00005
  14. [14] Toland J.F., Stokes waves, Topological Methods in Nonlinear Analysis7 (1996) 1-48, Topological Methods in Nonlinear Analysis8 (1997) 412-414. Zbl0897.35067MR1422004
  15. [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. Zbl0976.35052MR1792729
  16. [16] Toland J.F., On a pseudo-differential equation for Stokes waves, Arch. Rational Mech. Anal.162 (2002) 179-189. Zbl1028.35126MR1897380
  17. [17] Torchinsky A., Real-Variable Methods in Harmonic Analysis, Academic Press, Orlando, 1986. Zbl0621.42001MR869816
  18. [18] Zygmund A., Trigonometric Series I & II, Cambridge University Press, Cambridge, 1959. Zbl0367.42001MR107776

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