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  • Massimiliano Berti
  • Jean-Marc Delort
Chapter
  • 240 Downloads
Part of the Lecture Notes of the Unione Matematica Italiana book series (UMILN, volume 24)

Abstract

This second chapter is devoted to the statement of the main theorem we shall establish. The goal of the book is to prove that, for any arbitrary integer N, the capillary-gravity water waves equations, with periodic, even initial data, smooth enough and of small size 𝜖, have a solution defined on a time interval of length cN𝜖N, if the gravity-capillary parameters are taken outside a subset of zero measure.

References

  1. 26.
    Craig, W., Sulem, C.: Numerical simulation of gravity waves. J. Comput. Phys. 108(1), 73–83 (1993).  https://doi.org/10.1006/jcph.1993.1164 MathSciNetCrossRefGoogle Scholar
  2. 55.
    Lannes, D.: The Water Waves Problem. Mathematical Surveys and Monographs, vol. 188. American Mathematical Society, Providence, RI (2013).  https://doi.org/10.1090/surv/188. Mathematical analysis and asymptotics
  3. 68.
    Zakharov, V.E.: Stability of periodic waves of finite amplitude on the surface of a deep fluid. J. Appl. Mech. Tech. Phys. 9(2), 190–194 (1968)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Massimiliano Berti
    • 1
  • Jean-Marc Delort
    • 2
  1. 1.Department of MathematicsInternational School for Advanced Studies SISSATriesteItaly
  2. 2.LAGASorbonne Paris-Cité/University Paris 13VilletaneuseFrance

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