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 c N 𝜖 −N, if the gravity-capillary parameters are taken outside a subset of zero measure.
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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
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
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)
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Berti, M., Delort, JM. (2018). Main Result. In: Almost Global Solutions of Capillary-Gravity Water Waves Equations on the Circle. Lecture Notes of the Unione Matematica Italiana, vol 24. Springer, Cham. https://doi.org/10.1007/978-3-319-99486-4_2
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