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On the regularity of steady periodic stratified water waves
On the formation of singularities for surface water waves
| 1. | Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, United States |
References:
| [1] |
C. Amick, L. E. Fraenkel and J. F. Toland, On the Stokes conjecture for the wave of extreme form,, Acta Math., 148 (1982), 193. Google Scholar |
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A. Castro, D. Córdoba, C. Fefferman, F. Gancedo and J. Gómez-Serrano, Splash singularity for water waves,, preprint, (2011). Google Scholar |
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Adrian Constantin and Joachim Escher, Wave breaking for nonlinear nonlocal shallow water equations,, Acta Math., 181 (1998), 229. Google Scholar |
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H. Dong, D. Du and D. Li, Finite time singularities and global well-posedness for fractal Burgers equations,, Indiana Univ. Math. J., 58 (2009), 807. Google Scholar |
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Vera Mikyoung Hur, Gain of regularity for water waves with surface tension: a model equation,, preprint, (2011). Google Scholar |
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Michael Selwyn Longuet-Higgins, On the forming of sharp corners at a free surface,, Proc. R. Soc. Lond. A, 371 (1980), 453. Google Scholar |
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Michael Selwyn Longuet-Higgins, On the overturning of gravity waves,, Proc. R. Soc. Lond. A, 376 (1981), 377. Google Scholar |
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P. I. Naumkin and I. A. Shishmarev, "Nonlinear Nonlocal Equations in the Theory of Waves,", Translations of Mathematical Monographs, (1994). Google Scholar |
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D. Howell Peregrine, Breaking waves on beaches,, Ann. Rev. Fluid Mech., 15 (1983), 149. Google Scholar |
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J.-B. Song and M. L. Banner, On determining the onset and strength of breaking for deep water waves. Part I: Unforced irrotational wave groups,, Journal of Physical Oceanography, 32 (2002), 2541. Google Scholar |
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R. Thom, "Structural Stability and Morphogenesis,", Benjamin, (1975). Google Scholar |
| [12] |
Milton Van Dyke, "An Album of Fluid Motion,", Parabolic Press, (1982). Google Scholar |
| [13] |
Gerald Bereford Whitham, Variational methods and applications to water waves,, Hyperbolic equations and waves (Rencontre, (1968), 153. Google Scholar |
| [14] |
Gerald Beresford Whitham, "Linear and Nonlinear Waves,", Reprint of the 1974 original. Pure and Applied Mathematics, (1974). Google Scholar |
| [15] |
Sijue Wu, Well-posedness in Sobolev spaces of the full water wave problem in 2-D,, Invent. Math., 130 (1997), 39. Google Scholar |
| [16] |
Sijue Wu, Well-posedness in Sobolev spaces of the full water wave problem in 3-D,, J. Amer. Math. Soc., 12 (1999), 445. Google Scholar |
| [17] |
Sijue Wu, Almost global wellposedness of the 2-D full water wave problem,, Invent. Math., 177 (2009), 45. Google Scholar |
| [18] |
E. C. Zeeman, Breaking of waves,, Warwick Symposium on Differential Equations and Dynamical Systems, 206 (1971), 2. Google Scholar |
| [19] |
Antoni Zygmund, "Trigonometric Series,", Volume 2, (1968). Google Scholar |
show all references
References:
| [1] |
C. Amick, L. E. Fraenkel and J. F. Toland, On the Stokes conjecture for the wave of extreme form,, Acta Math., 148 (1982), 193. Google Scholar |
| [2] |
A. Castro, D. Córdoba, C. Fefferman, F. Gancedo and J. Gómez-Serrano, Splash singularity for water waves,, preprint, (2011). Google Scholar |
| [3] |
Adrian Constantin and Joachim Escher, Wave breaking for nonlinear nonlocal shallow water equations,, Acta Math., 181 (1998), 229. Google Scholar |
| [4] |
H. Dong, D. Du and D. Li, Finite time singularities and global well-posedness for fractal Burgers equations,, Indiana Univ. Math. J., 58 (2009), 807. Google Scholar |
| [5] |
Vera Mikyoung Hur, Gain of regularity for water waves with surface tension: a model equation,, preprint, (2011). Google Scholar |
| [6] |
Michael Selwyn Longuet-Higgins, On the forming of sharp corners at a free surface,, Proc. R. Soc. Lond. A, 371 (1980), 453. Google Scholar |
| [7] |
Michael Selwyn Longuet-Higgins, On the overturning of gravity waves,, Proc. R. Soc. Lond. A, 376 (1981), 377. Google Scholar |
| [8] |
P. I. Naumkin and I. A. Shishmarev, "Nonlinear Nonlocal Equations in the Theory of Waves,", Translations of Mathematical Monographs, (1994). Google Scholar |
| [9] |
D. Howell Peregrine, Breaking waves on beaches,, Ann. Rev. Fluid Mech., 15 (1983), 149. Google Scholar |
| [10] |
J.-B. Song and M. L. Banner, On determining the onset and strength of breaking for deep water waves. Part I: Unforced irrotational wave groups,, Journal of Physical Oceanography, 32 (2002), 2541. Google Scholar |
| [11] |
R. Thom, "Structural Stability and Morphogenesis,", Benjamin, (1975). Google Scholar |
| [12] |
Milton Van Dyke, "An Album of Fluid Motion,", Parabolic Press, (1982). Google Scholar |
| [13] |
Gerald Bereford Whitham, Variational methods and applications to water waves,, Hyperbolic equations and waves (Rencontre, (1968), 153. Google Scholar |
| [14] |
Gerald Beresford Whitham, "Linear and Nonlinear Waves,", Reprint of the 1974 original. Pure and Applied Mathematics, (1974). Google Scholar |
| [15] |
Sijue Wu, Well-posedness in Sobolev spaces of the full water wave problem in 2-D,, Invent. Math., 130 (1997), 39. Google Scholar |
| [16] |
Sijue Wu, Well-posedness in Sobolev spaces of the full water wave problem in 3-D,, J. Amer. Math. Soc., 12 (1999), 445. Google Scholar |
| [17] |
Sijue Wu, Almost global wellposedness of the 2-D full water wave problem,, Invent. Math., 177 (2009), 45. Google Scholar |
| [18] |
E. C. Zeeman, Breaking of waves,, Warwick Symposium on Differential Equations and Dynamical Systems, 206 (1971), 2. Google Scholar |
| [19] |
Antoni Zygmund, "Trigonometric Series,", Volume 2, (1968). Google Scholar |
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