T. Alazard and P. Baldi, Gravity Capillary Standing Water Waves, Archive for Rational Mechanics and Analysis, vol.24, issue.4, pp.741-830, 2015.
DOI : 10.1088/0951-7715/24/4/010

T. Alazard, N. Burq, and C. Zuily, On the water-wave equations with surface tension, Duke Mathematical Journal, vol.158, issue.3, pp.413-499, 2011.
DOI : 10.1215/00127094-1345653

T. Alazard, N. Burq, and C. Zuily, Strichartz estimates for water waves, Annales scientifiques de l'??cole normale sup??rieure, vol.44, issue.5, pp.855-903, 2011.
DOI : 10.24033/asens.2156
URL : https://hal.archives-ouvertes.fr/hal-00452071

T. Alazard, N. Burq, and C. Zuily, On the Cauchy problem for gravity water waves, Inventiones mathematicae, vol.61, issue.7, pp.71-163, 2014.
DOI : 10.1002/cpa.20226
URL : https://hal.archives-ouvertes.fr/hal-00760452

T. Alazard, N. Burq, and C. Zuily, Cauchy theory for the gravity water waves system with non-localized initial data, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.33, issue.2, pp.337-395, 2016.
DOI : 10.1016/j.anihpc.2014.10.004

T. Alazard and J. Delort, Global solutions and asymptotic behavior for two dimensional gravity water waves, Annales scientifiques de l'??cole normale sup??rieure, vol.48, issue.5, pp.1149-1238, 2015.
DOI : 10.24033/asens.2268
URL : https://hal.archives-ouvertes.fr/hal-00844304

T. Alazard and J. Delort, Sobolev estimates for two dimensional gravity water waves, Astérisque, issue.374, p.241, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00844205

T. Alazard and G. Métivier, Paralinearization of the Dirichlet to Neumann Operator, and Regularity of Three-Dimensional Water Waves, Communications in Partial Differential Equations, vol.1, issue.12, pp.10-121632, 2009.
DOI : 10.1090/S0894-0347-99-00290-8
URL : https://hal.archives-ouvertes.fr/hal-00354473

S. Alinhac, Paracomposition et operateurs paradifferentiels, Communications in Partial Differential Equations, vol.81, issue.1, pp.87-121, 1986.
DOI : 10.1080/03605308608820419

S. Alinhac, Ondes de raréfaction pour des systèmes quasi-linéaires hyperboliques multidimensionnels, Journées " Équations aux Dérivées Partielles, 1988.

D. M. Ambrose, Well-Posedness of Vortex Sheets with Surface Tension, SIAM Journal on Mathematical Analysis, vol.35, issue.1, pp.211-244, 2003.
DOI : 10.1137/S0036141002403869

D. M. Ambrose and N. Masmoudi, The zero surface tension limit two-dimensional water waves, Communications on Pure and Applied Mathematics, vol.23, issue.10, pp.1287-1315, 2005.
DOI : 10.1002/cpa.20085

P. Baldi, M. Berti, E. Haus, and R. Montalto, Time quasi-periodic gravity water waves in finite depth, Inventiones mathematicae, vol.24, issue.4, 2017.
DOI : 10.1088/0951-7715/24/4/010

M. Berti and J. Delort, Almost global existence of solutions for capillary-gravity water waves equations with periodic spatial boundary conditions, 2017.

M. Berti and R. Montalto, KAM for gravity capillary water waves, Memoires of AMS, 2017.

J. Bony, Calcul symbolique et propagation des singularit??s pour les ??quations aux d??riv??es partielles non lin??aires, Annales scientifiques de l'??cole normale sup??rieure, vol.14, issue.2, pp.209-246, 1981.
DOI : 10.24033/asens.1404

D. Christodoulou and H. Lindblad, On the motion of the free surface of a liquid, Communications on Pure and Applied Mathematics, vol.18, issue.12, pp.1536-1602, 2000.
DOI : 10.1007/978-3-642-61798-0

D. Coutand and S. Shkoller, Well-posedness of the free-surface incompressible Euler equations with or without surface tension, Journal of the American Mathematical Society, vol.20, issue.03, pp.829-930, 2007.
DOI : 10.1090/S0894-0347-07-00556-5

W. Craig, An existence theory for water waves and the boussinesq and korteweg-devries scaling limits, Communications in Partial Differential Equations, vol.5, issue.3, pp.787-1003, 1985.
DOI : 10.1007/BF01086739

W. Craig and C. Sulem, Numerical Simulation of Gravity Waves, Journal of Computational Physics, vol.108, issue.1, pp.73-83, 1993.
DOI : 10.1006/jcph.1993.1164

J. Delort, Long-time Sobolev stability for small solutions of quasilinear Klein-Gordon equations on the circle, Trans. Amer. Math. Soc, issue.8, pp.3614299-4365, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00157765

J. Delort, A quasi-linear Birkhoff normal forms method. Application to the quasi-linear Klein-Gordon equation on S 1, Astérisque, issue.341, p.113, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00354876

J. Delort, Quasi-linear perturbations of Hamiltonian Klein-Gordon equations on spheres, Memoirs of the American Mathematical Society, vol.234, issue.1103, p.80, 1103.
DOI : 10.1090/memo/1103
URL : https://hal.archives-ouvertes.fr/hal-00643474

Y. Deng, A. D. Ionescu, B. Pausader, and F. Pusateri, Global solutions of the gravity-capilarity water waves system in 3 dimensions, 2015.

P. Germain, N. Masmoudi, and J. Shatah, Global solutions for 2D quadratic Schr??dinger equations, Journal de Math??matiques Pures et Appliqu??es, vol.97, issue.5, pp.505-543, 2012.
DOI : 10.1016/j.matpur.2011.09.008
URL : https://doi.org/10.1016/j.matpur.2011.09.008

P. Germain, N. Masmoudi, and J. Shatah, Global solutions for the gravity water waves equation in dimension 3, Annals of Mathematics, vol.175, issue.2, pp.691-754, 2012.
DOI : 10.4007/annals.2012.175.2.6

B. Harrop-griffiths, M. Ifrim, and D. Tataru, Finite Depth Gravity Water Waves in Holomorphic Coordinates, Annals of PDE, vol.9, issue.2, 2017.
DOI : 10.1007/BF00913182
URL : https://cloudfront.escholarship.org/dist/prd/content/qt4fw309gq/qt4fw309gq.pdf?t=ocf7k8

J. K. Hunter, M. Ifrim, and D. Tataru, Two Dimensional Water Waves in Holomorphic Coordinates, Communications in Mathematical Physics, vol.61, issue.7, pp.483-552, 2016.
DOI : 10.1002/cpa.20226
URL : http://arxiv.org/pdf/1401.1252

J. K. Hunter, M. Ifrim, D. Tataru, and T. K. Wong, Long time solutions for a Burgers-Hilbert equation via a modified energy method, Proc. Amer, pp.3407-3412, 2015.
DOI : 10.1090/proc/12215
URL : http://arxiv.org/pdf/1301.1947.pdf

M. Ifrim and D. Tataru, Global bounds for the cubic nonlinear Schr??dinger equation (NLS) in one space dimension, Nonlinearity, vol.28, issue.8, pp.2661-2675, 2015.
DOI : 10.1088/0951-7715/28/8/2661
URL : http://arxiv.org/pdf/1404.7581

M. Ifrim and D. Tataru, Two dimensional gravity water waves with constant vorticity: I. cubic lifespan, 2015.
DOI : 10.2140/apde.2019.12.903
URL : http://arxiv.org/pdf/1510.07732

M. Ifrim and D. Tataru, Two dimensional water waves in holomorphic coordinates II: global solutions, Bulletin de la Société mathématique de France, vol.144, issue.2, pp.369-394, 2016.
DOI : 10.24033/bsmf.2717
URL : https://cloudfront.escholarship.org/dist/prd/content/qt3q7856k3/qt3q7856k3.pdf?t=ocf6q2

M. Ifrim and D. Tataru, The Lifespan of Small Data Solutions in Two Dimensional Capillary Water Waves, Archive for Rational Mechanics and Analysis, vol.23, issue.4, pp.1279-1346, 2017.
DOI : 10.1215/kjm/1250521429

A. D. Ionescu and F. Pusateri, Global regularity for 2d water waves with surface tension, 2015.
DOI : 10.1090/memo/1227
URL : http://arxiv.org/pdf/1408.4428

A. D. Ionescu and F. Pusateri, Global solutions for the gravity water waves system in 2d, Inventiones mathematicae, vol.184, issue.1, pp.653-804, 2015.
DOI : 10.1007/s00222-010-0288-1

G. Iooss, P. I. Plotnikov, and J. F. Toland, Standing Waves on an Infinitely Deep Perfect Fluid Under Gravity, Archive for Rational Mechanics and Analysis, vol.2, issue.3, pp.367-478, 2005.
DOI : 10.1016/j.crma.2004.01.002
URL : https://hal.archives-ouvertes.fr/hal-00009222

D. Lannes, Well-posedness of the water waves equations, J. Amer. Math. Soc, vol.18, issue.3, pp.605-654, 2005.
DOI : 10.1090/surv/188/04
URL : https://hal.archives-ouvertes.fr/hal-00258834

D. L. Germain, . Masmoudi, and . Shatah, Space-time resonances, Journ??es ??quations aux d??riv??es partielles
DOI : 10.5802/jedp.65
URL : https://hal.archives-ouvertes.fr/hal-00873086

. Astérisque, Exp. No. 1053, ix, pp.355-3882012, 2013.

D. Lannes, The water waves problem, volume 188 of Mathematical Surveys and Monographs

H. Lindblad, Well-posedness for the motion of an incompressible liquid with free surface boundary, Annals of Mathematics, vol.162, issue.1, pp.109-194, 2005.
DOI : 10.4007/annals.2005.162.109

V. I. Nalimov, The Cauchy-Poisson problem, Vyp. 18 Dinamika ?idkost. so Svobod. Granicami), pp.104-210, 1974.

T. Ozawa, K. Tsutaya, and Y. Tsutsumi, Remarks on the Klein-Gordon equation with quadratic nonlinearity in two space dimensions, In Nonlinear waves GAKUTO Internat. Ser. Math. Sci. Appl. Gakk¯ otosho, vol.10, pp.383-392, 1995.

P. I. Plotnikov and J. F. Toland, Nash-Moser Theory for Standing Water Waves, Archive for Rational Mechanics and Analysis, vol.159, issue.1, pp.1-83, 2001.
DOI : 10.1007/PL00004246

J. Shatah, Normal forms and quadratic nonlinear Klein-Gordon equations, Communications on Pure and Applied Mathematics, vol.41, issue.5, pp.685-696, 1985.
DOI : 10.1007/978-1-4684-0147-9

J. Shatah and C. Zeng, Geometry and a priori estimates for free boundary problems of the Euler's equation, Communications on Pure and Applied Mathematics, vol.23, issue.170, pp.698-744, 2008.
DOI : 10.5802/aif.233

J. Shatah and C. Zeng, A priori estimates for fluid interface problems, Communications on Pure and Applied Mathematics, vol.59, issue.6, pp.848-876, 2008.
DOI : 10.5802/aif.233

J. Shatah and C. Zeng, Local Well-Posedness for Fluid Interface Problems, Archive for Rational Mechanics and Analysis, vol.61, issue.7, pp.653-705, 2011.
DOI : 10.1002/cpa.20226

N. Totz, A Justification of the Modulation Approximation to the 3D Full Water Wave Problem, Communications in Mathematical Physics, vol.9, issue.2, pp.369-443, 2015.
DOI : 10.1090/S0894-0347-99-00290-8

N. Totz and S. Wu, A Rigorous Justification of the Modulation Approximation to the 2D Full Water Wave Problem, Communications in Mathematical Physics, vol.9, issue.2, pp.817-883, 2012.
DOI : 10.1007/s00222-010-0288-1

X. Wang, Global Infinite Energy Solutions for the 2D Gravity Water Waves System, Communications on Pure and Applied Mathematics, vol.9, issue.2, 2015.
DOI : 10.1007/BF00913182

X. Wang, Global solutions for the 3d water waves system above a flat bottom, 2015.

X. Wang, Global regularity for the 3d finite depth capillary water waves, 2017.

X. Wang, On the 3-dimensional water waves system above a flat bottom, Analysis & PDE, vol.18, issue.4, pp.893-928, 2017.
DOI : 10.1007/BF00913182

S. Wu, Well-posedness in Sobolev spaces of the full water wave problem in 2-D, Inventiones Mathematicae, vol.130, issue.1, pp.39-72, 1997.
DOI : 10.1007/s002220050177

S. Wu, Well-posedness in Sobolev spaces of the full water wave problem in 2-D, Inventiones Mathematicae, vol.130, issue.1, pp.445-495, 1999.
DOI : 10.1007/s002220050177

S. Wu, Almost global wellposedness of the 2-D full water wave problem, Inventiones mathematicae, vol.61, issue.7, pp.45-135, 2009.
DOI : 10.1017/CBO9780511530029
URL : http://arxiv.org/pdf/0910.2473

S. Wu, Global wellposedness of the 3-D full water wave problem, Inventiones mathematicae, vol.61, issue.7, pp.125-220, 2011.
DOI : 10.1002/cpa.20226
URL : http://arxiv.org/pdf/0910.2473.pdf

H. Yosihara, Gravity waves on the free surface of an incompressible perfect fluid of finite depth, Publications of the Research Institute for Mathematical Sciences, vol.18, issue.1, pp.49-96, 1982.
DOI : 10.2977/prims/1195184016

V. E. Zakharov, Stability of periodic waves of finite amplitude on the surface of a deep fluid, Journal of Applied Mechanics and Technical Physics, vol.10, issue.no. 4, pp.190-1943, 1968.
DOI : 10.1007/BF00913182