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Volumn 39, Issue 6, 2019, Pages 3123-3147

Sufficiently strong dispersion removes ill-posedness in truncated series models of water waves

Author keywords

Hydroelastic; Operator expansions; Paradifferential calculus; Water waves; Well posedness

Indexed keywords


EID: 85063788262     PISSN: 10780947     EISSN: 15535231     Source Type: Journal    
DOI: 10.3934/dcds.2019129     Document Type: Article
Times cited : (3)

References (38)
  • 1
    • 79959880152 scopus 로고    scopus 로고
    • On the water-wave equations with surface tension
    • T. Alazard, N. Burq and C. Zuily, On the water-wave equations with surface tension, Duke Math. J., 158 (2011), 413-499.
    • (2011) Duke Math. J. , vol.158 , pp. 413-499
    • Alazard, T.1    Burq, N.2    Zuily, C.3
  • 4
    • 26944460000 scopus 로고    scopus 로고
    • The zero surface tension limit of two-dimensional water waves
    • D. Ambrose and N. Masmoudi, The zero surface tension limit of two-dimensional water waves, Comm. Pure Appl. Math., 58 (2005), 1287-1315.
    • (2005) Comm. Pure Appl. Math. , vol.58 , pp. 1287-1315
    • Ambrose, D.1    Masmoudi, N.2
  • 5
    • 67249144683 scopus 로고    scopus 로고
    • The zero surface tension limit of three-dimensional water waves
    • D. Ambrose and N. Masmoudi, The zero surface tension limit of three-dimensional water waves, Indiana Univ. Math. J., 58 (2009), 479-521.
    • (2009) Indiana Univ. Math. J. , vol.58 , pp. 479-521
    • Ambrose, D.1    Masmoudi, N.2
  • 6
    • 85015628650 scopus 로고    scopus 로고
    • Well-posedness of two-dimensional hydroelastic waves
    • D. Ambrose and M. Siegel, Well-posedness of two-dimensional hydroelastic waves, Proc. Roy. Soc. Edinburgh Sect. A, 147 (2017), 529-570.
    • (2017) Proc. Roy. Soc. Edinburgh Sect. A , vol.147 , pp. 529-570
    • Ambrose, D.1    Siegel, M.2
  • 8
    • 84940386316 scopus 로고    scopus 로고
    • Local existence theory for derivative nonlinear Schrödinger equations with noninteger power nonlinearities
    • D. Ambrose and G. Simpson, Local existence theory for derivative nonlinear Schrödinger equations with noninteger power nonlinearities, SIAM J. Math. Anal., 47 (2015), 2241-2264.
    • (2015) SIAM J. Math. Anal. , vol.47 , pp. 2241-2264
    • Ambrose, D.1    Simpson, G.2
  • 9
    • 77955068691 scopus 로고    scopus 로고
    • Bifurcation and secondary bifurcation of heavy periodic hydroelastic travelling waves
    • P. Baldi and J. Toland, Bifurcation and secondary bifurcation of heavy periodic hydroelastic travelling waves, Interfaces Free Bound., 12 (2010), 1-22.
    • (2010) Interfaces Free Bound. , vol.12 , pp. 1-22
    • Baldi, P.1    Toland, J.2
  • 10
    • 0031079913 scopus 로고    scopus 로고
    • Reappraisal of the Kelvin-Helmholtz problem. II. Interaction of the Kelvin-Helmholtz, superharmonic and Benjamin-Feir instabilities
    • T. Benjamin and T. Bridges, Reappraisal of the Kelvin-Helmholtz problem. II. Interaction of the Kelvin-Helmholtz, superharmonic and Benjamin-Feir instabilities, J. Fluid Mech., 333 (1997), 327-373.
    • (1997) J. Fluid Mech. , vol.333 , pp. 327-373
    • Benjamin, T.1    Bridges, T.2
  • 11
    • 0001191104 scopus 로고
    • Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires
    • URL
    • J.-M. Bony, Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires, Ann. Sci. École Norm. Sup. (4), 14 (1981), 209-246, URL http: //www.numdam.org/item?id=ASENS-1981-4-14-2-209-0.
    • (1981) Ann. Sci. École Norm. Sup. (4) , vol.14 , pp. 209-246
    • Bony, J.-M.1
  • 12
    • 0001747831 scopus 로고
    • Singular solutions and ill-posedness for the evolution of vortex sheets
    • R. Caisch and O. Orellana, Singular solutions and ill-posedness for the evolution of vortex sheets, SIAM J. Math. Anal., 20 (1989), 293-307.
    • (1989) SIAM J. Math. Anal. , vol.20 , pp. 293-307
    • Caisch, R.1    Orellana, O.2
  • 14
    • 84968508844 scopus 로고
    • Local smoothing properties of dispersive equations
    • P. Constantin and J.-C. Saut, Local smoothing properties of dispersive equations, J. Amer. Math. Soc., 1 (1988), 413-439.
    • (1988) J. Amer. Math. Soc. , vol.1 , pp. 413-439
    • Constantin, P.1    Saut, J.-C.2
  • 15
    • 30544433668 scopus 로고    scopus 로고
    • Hamiltonian long-wave expansions for free surfaces and interfaces
    • W. Craig, P. Guyenne and H. Kalisch, Hamiltonian long-wave expansions for free surfaces and interfaces, Comm. Pure Appl. Math., 58 (2005), 1587-1641.
    • (2005) Comm. Pure Appl. Math. , vol.58 , pp. 1587-1641
    • Craig, W.1    Guyenne, P.2    Kalisch, H.3
  • 16
    • 76349125095 scopus 로고    scopus 로고
    • Water waves over a random bottom
    • W. Craig, P. Guyenne and C. Sulem, Water waves over a random bottom, J. Fluid Mech., 640 (2009), 79-107.
    • (2009) J. Fluid Mech. , vol.640 , pp. 79-107
    • Craig, W.1    Guyenne, P.2    Sulem, C.3
  • 17
    • 0002686768 scopus 로고
    • Numerical simulation of gravity waves
    • W. Craig and C. Sulem, Numerical simulation of gravity waves, J. Comput. Phys., 108 (1993), 73-83.
    • (1993) J. Comput. Phys. , vol.108 , pp. 73-83
    • Craig, W.1    Sulem, C.2
  • 19
    • 38849134959 scopus 로고    scopus 로고
    • Theory of weakly damped free-surface ows: A new formulation based on potential ow solutions
    • F. Dias, A. Dyachenko and V. Zakharov, Theory of weakly damped free-surface ows: A new formulation based on potential ow solutions, Phys. Lett. A, 372 (2008), 1297-1302.
    • (2008) Phys. Lett. A , vol.372 , pp. 1297-1302
    • Dias, F.1    Dyachenko, A.2    Zakharov, V.3
  • 20
    • 84994123732 scopus 로고    scopus 로고
    • Variational existence theory for hydroelastic solitary waves
    • M. Groves, B. Hewer and E. Wahlén, Variational existence theory for hydroelastic solitary waves, C. R. Math. Acad. Sci. Paris, 354 (2016), 1078-1086.
    • (2016) C. R. Math. Acad. Sci. Paris , vol.354 , pp. 1078-1086
    • Groves, M.1    Hewer, B.2    Wahlén, E.3
  • 21
    • 84870809773 scopus 로고    scopus 로고
    • Computations of fully nonlinear hydroelastic solitary waves on deep water
    • P. Guyenne and E. Pǎrǎu, Computations of fully nonlinear hydroelastic solitary waves on deep water, J. Fluid Mech., 713 (2012), 307-329.
    • (2012) J. Fluid Mech. , vol.713 , pp. 307-329
    • Guyenne, P.1    Pǎrǎu, E.2
  • 22
    • 0003764816 scopus 로고    scopus 로고
    • of Mathématiques & Applications (Berlin) [Mathematics & Applications], Springer-Verlag, Berlin
    • L. Hörmander, Lectures on Nonlinear Hyperbolic Differential Equations, vol. 26 of Mathématiques & Applications (Berlin) [Mathematics & Applications], Springer-Verlag, Berlin, 1997.
    • (1997) Lectures on Nonlinear Hyperbolic Differential Equations , vol.26
    • Hörmander, L.1
  • 23
    • 0002362136 scopus 로고
    • On the Cauchy problem for the (generalized) Korteweg-de Vries equation
    • of Adv. Math. Suppl. Stud., Academic Press, New York
    • T. Kato, On the Cauchy problem for the (generalized) Korteweg-de Vries equation, in Studies in Applied Mathematics, vol. 8 of Adv. Math. Suppl. Stud., Academic Press, New York, 1983, 93-128.
    • (1983) Studies in Applied Mathematics , vol.8 , pp. 93-128
    • Kato, T.1
  • 24
    • 22544482964 scopus 로고    scopus 로고
    • Well-posedness of the water-waves equations
    • electronic
    • D. Lannes, Well-posedness of the water-waves equations, J. Amer. Math. Soc., 18 (2005), 605-654 (electronic).
    • (2005) J. Amer. Math. Soc. , vol.18 , pp. 605-654
    • Lannes, D.1
  • 25
    • 84899790304 scopus 로고    scopus 로고
    • of Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, Mathematical analysis and asymptotics
    • D. Lannes, The Water Waves Problem, vol. 188 of Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, 2013, Mathematical analysis and asymptotics.
    • (2013) The Water Waves Problem , vol.188
    • Lannes, D.1
  • 27
    • 85008506415 scopus 로고    scopus 로고
    • Well-posedness of two-dimensional hydroelastic waves with mass
    • URL, In press
    • S. Liu and D. Ambrose, Well-posedness of two-dimensional hydroelastic waves with mass, J. Differential Equations, 262 (2017), 4656-4699, URL http://www.sciencedirect.com/ science/article/pii/S0022039616304879, In press.
    • (2017) J. Differential Equations , vol.262 , pp. 4656-4699
    • Liu, S.1    Ambrose, D.2
  • 29
    • 0025476908 scopus 로고
    • The effects of truncation on surface-wave Hamiltonians
    • D. Milder, The effects of truncation on surface-wave Hamiltonians, J. Fluid Mech., 217 (1990), 249-262.
    • (1990) J. Fluid Mech. , vol.217 , pp. 249-262
    • Milder, D.1
  • 30
    • 78650859910 scopus 로고    scopus 로고
    • Spectral stability of traveling water waves: Eigenvalue collision, singularities, and direct numerical simulation
    • URL
    • D. Nicholls, Spectral stability of traveling water waves: Eigenvalue collision, singularities, and direct numerical simulation, Phys. D, 240 (2011), 376-381, URL http://www.sciencedirect. com/science/article/pii/S0167278910002630.
    • (2011) Phys. D , vol.240 , pp. 376-381
    • Nicholls, D.1
  • 32
    • 0001648070 scopus 로고
    • Convergence of solutions to nonlinear dispersive equations
    • M. Schonbek, Convergence of solutions to nonlinear dispersive equations, Comm. Partial Differential Equations, 7 (1982), 959-1000.
    • (1982) Comm. Partial Differential Equations , vol.7 , pp. 959-1000
    • Schonbek, M.1
  • 33
    • 85063790791 scopus 로고
    • of Progress in Mathematics, Birkhäuser Boston, Inc., Boston, MA
    • M. Taylor, Pseudodifferential Operators and Nonlinear PDE, vol. 100 of Progress in Mathematics, Birkhäuser Boston, Inc., Boston, MA, 1991.
    • (1991) Pseudodifferential Operators and Nonlinear PDE , vol.100
    • Taylor, M.1
  • 35
    • 85106769330 scopus 로고    scopus 로고
    • Comparison of five methods of computing the Dirichlet-Neumann operator for the water wave problem
    • of Contemp. Math., Amer. Math. Soc., Providence, RI
    • J. Wilkening and V. Vasan, Comparison of five methods of computing the Dirichlet-Neumann operator for the water wave problem, in Nonlinear wave equations: analytic and compu- tational techniques, vol. 635 of Contemp. Math., Amer. Math. Soc., Providence, RI, 2015, 175-210.
    • (2015) Nonlinear Wave Equations: Analytic and Compu- Tational Techniques , vol.635 , pp. 175-210
    • Wilkening, J.1    Vasan, V.2
  • 36
    • 0031506263 scopus 로고    scopus 로고
    • Well-posedness in Sobolev spaces of the full water wave problem in 2-D
    • S. Wu, Well-posedness in Sobolev spaces of the full water wave problem in 2-D, Invent. Math., 130 (1997), 39-72.
    • (1997) Invent. Math. , vol.130 , pp. 39-72
    • Wu, S.1
  • 37
    • 0033446356 scopus 로고    scopus 로고
    • Well-posedness in Sobolev spaces of the full water wave problem in 3-D
    • S. Wu, Well-posedness in Sobolev spaces of the full water wave problem in 3-D, J. Amer. Math. Soc., 12 (1999), 445-495.
    • (1999) J. Amer. Math. Soc. , vol.12 , pp. 445-495
    • Wu, S.1
  • 38
    • 34250447917 scopus 로고
    • Stability of periodic waves of finite amplitude on the surface of a deep uid
    • V. Zakharov, Stability of periodic waves of finite amplitude on the surface of a deep uid, Journal of Applied Mechanics and Technical Physics, 9 (1968), 190-194.
    • (1968) Journal of Applied Mechanics and Technical Physics , vol.9 , pp. 190-194
    • Zakharov, V.1


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