L. Abdelouhab, J. Bona, M. Felland, and J. Saut, Nonlocal models for nonlinear, dispersive waves, Physica D: Nonlinear Phenomena, vol.40, issue.3, pp.360-392, 1989.
DOI : 10.1016/0167-2789(89)90050-X

T. B. Benjamin, Internal waves of permanent form in fluids of great depth, Journal of Fluid Mechanics, vol.45, issue.03, pp.559-592, 1967.
DOI : 10.1017/S002211206700103X

J. Bourgain, Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations, Geometric and Functional Analysis, vol.34, issue.1, pp.107-156, 1993.
DOI : 10.1007/BF01896020

N. Burq and F. Planchon, On well-posedness for the Benjamin???Ono equation, Mathematische Annalen, vol.123, issue.5, pp.497-542, 2008.
DOI : 10.1007/s00208-007-0150-y
URL : https://hal.archives-ouvertes.fr/hal-00017561

J. Ginibre, Leprobì eme de Cauchy pour des EDP semi-linéaires périodiques en variables d'espace (d'après Bourgain), in Séminaire Bourbaki 796, Astérique, vol.237, pp.163-187, 1995.

L. Grafacos, Classical and Modern Fourier Analysis, Pearson, 2004.

Z. Guo, Local wellposedness and a priori bounds for the modified Benjamin-Ono equation, Advances in Differential Equations, pp.11-12, 2011.

S. Herr, On the Cauchy problem for the derivative nonlinear Schrödinger equation with periodic boundary condition, Int. Math. Res. Not, 2006.

A. Ionescu and C. Kenig, Global well-posedness of the Benjamin--Ono equation in low-regularity spaces, Journal of the American Mathematical Society, vol.20, issue.03, pp.753-798, 2007.
DOI : 10.1090/S0894-0347-06-00551-0

R. and I. Jr, On the Cauchy problem for the Benjamin-Ono equation, Comm. Part. Diff. Eqs, vol.11, pp.1031-1081, 1986.

T. Kato and G. Ponce, Commutator estimates and the euler and navier-stokes equations, Communications on Pure and Applied Mathematics, vol.18, issue.7, pp.891-907, 1988.
DOI : 10.1002/cpa.3160410704

C. Kenig and K. Koenig, On the local well-posedness of the Benjamin-Ono and modified Benjamin-Ono equations, Mathematical Research Letters, vol.10, issue.6, pp.879-895, 2003.
DOI : 10.4310/MRL.2003.v10.n6.a13

C. Kenig, G. Ponce, and L. Vega, Well-posedness and scattering results for the generalized korteweg-de vries equation via the contraction principle, Communications on Pure and Applied Mathematics, vol.34, issue.4, pp.46-527, 1993.
DOI : 10.1002/cpa.3160460405

C. Kenig, G. Ponce, and L. Vega, On the generalized Benjamin-Ono equation, Transactions of the American Mathematical Society, vol.342, issue.1, pp.155-172, 1994.
DOI : 10.1090/S0002-9947-1994-1153015-4

C. Kenig and H. Takaoka, Global wellposedness of the modified Benjamin-Ono equation with initial data in H1/2, International Mathematics Research Notices, issue.2, pp.1-44, 2006.
DOI : 10.1155/IMRN/2006/95702

C. Kenig, Y. Martel, and L. Robbiano, Local well-posedness and blow up in the energy space for a class of L2 critical dispersion generalized Benjamin-Ono equations, Anal. Non Linaire, vol.28, pp.853-887, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00658956

H. Koch and N. Tzvetkov, On the local well-posedness of the Benjamin-Ono equation in H s (R), Int. Math. Res. Not, pp.1449-1464, 2003.

L. Molinet and D. Pilod, revisited, Analysis & PDE, vol.5, issue.2, pp.365-395, 2012.
DOI : 10.2140/apde.2012.5.365
URL : https://hal.archives-ouvertes.fr/hal-00499346

L. Molinet and F. Ribaud, Well-posedness results for the generalized Benjamin-Ono equation with arbitary large initial data, Int. Math. Res. Not, pp.3757-3795, 2004.

L. Molinet and F. Ribaud, Well-posedness results for the generalized Benjamin???Ono equation with small initial data, Journal de Math??matiques Pures et Appliqu??es, vol.83, issue.2, pp.277-311, 2004.
DOI : 10.1016/j.matpur.2003.11.005

L. Molinet, Global well-posedness in the energy space for the Benjamin???Ono equation on the circle, Mathematische Annalen, vol.1, issue.3, pp.353-383, 2007.
DOI : 10.1007/s00208-006-0038-2

L. Molinet, Global well-posedness in <i>L</i><sup xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> for the periodic Benjamin-Ono equation, American Journal of Mathematics, vol.130, issue.3, pp.635-683, 2008.
DOI : 10.1353/ajm.0.0001

L. Molinet and F. Ribaud, Well-posedness in H 1 for the (generalized) Benjamin-Ono equation on the circle, DCDS, vol.23, pp.1295-1311, 2009.

L. Molinet, Sharp ill-posedness result for the periodic Benjamin???Ono equation, Journal of Functional Analysis, vol.257, issue.11, pp.3488-3516, 2009.
DOI : 10.1016/j.jfa.2009.08.018
URL : https://hal.archives-ouvertes.fr/hal-00336559

H. Ono, Algebraic Solitary Waves in Stratified Fluids, Journal of the Physical Society of Japan, vol.39, issue.4, pp.1082-1091, 1975.
DOI : 10.1143/JPSJ.39.1082

G. Ponce, On the global well-posedness of the Benjamin-Ono equation, Diff. Int. Eqs, vol.4, pp.527-542, 1991.

T. Tao, ), Journal of Hyperbolic Differential Equations, vol.01, issue.01, pp.27-49, 2004.
DOI : 10.1142/S0219891604000032