H. Bahouri, J. Chemin, and R. Danchin, Fourier Analysis and non linear partial dierential equations, 2011.

J. Bourgain and N. Pavlovic, Ill-posedness of the Navier???Stokes equations in a critical space in 3D, Journal of Functional Analysis, vol.255, issue.9, pp.2233-2247, 2008.
DOI : 10.1016/j.jfa.2008.07.008

J. Chemin, ?? propos d'un probl??me de p??nalisation de type antisym??trique, Journal de Math??matiques Pures et Appliqu??es, vol.76, issue.9, pp.739-755, 1997.
DOI : 10.1016/S0021-7824(97)89967-9

J. Chemin and I. Gallagher, Large, global solutions to the Navier-Stokes equations, slowly varying in one direction. Transactions of the, pp.6-2859, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00182927

J. Chemin, I. Gallagher, and P. Zhang, On large perturbations to global solutions of the 3- D incompressible Navier-Stokes equations

A. Dutrifoy, A. Majda, and S. Schochet, A simple justication of the singular limit for equatorial shallow water dynamics, Communications on Pure and Applied Mathematics, 2008.

H. Fujita and T. Kato, On the Navier-Stokes initial value problem I . Archive for Rational Mechanics and Analysis, pp.269-315, 1964.

I. Gallagher and L. Saint-raymond, Mathematical study of the betaplane model, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00022119

I. Gallagher and L. Saint-raymond, On the inuence of the Earth's rotation on geophysical ows. Handbook of Mathematical Fluid Dynamics, pp.201-239, 2007.

I. Gallagher, Asymptotics for hyperbolic equations with a skew-symmetric perturbation Hyperbolic problems : theory, numerics, applications, pp.369-373, 1998.

I. Gallagher, D. Iftimie, and F. Planchon, Asymptotics and stability for global solutions to the Navier-Stokes equations. Annales de l'Institut fourier, pp.2075-2083, 2003.

P. Germain, The second iterate for the Navier???Stokes equation, Journal of Functional Analysis, vol.255, issue.9, 2008.
DOI : 10.1016/j.jfa.2008.07.014

Y. Giga and T. Miyakawa, Solutions in L r of the Navier-Stokes initial value problem. Archive for Rational Mechanics and Analysis, pp.3-267, 1985.

A. Gill, Atmosphere-Ocean Dynamics, International Geophysics Series, vol.30, 1982.

H. Greenspan, The Theory of rotating uids, Cambridge monographs on mechanisms and applied mathematics, 1969.

E. Grenier, Oscillatory perturbations of the Navier Stokes equations, Journal de Math??matiques Pures et Appliqu??es, vol.76, issue.6, pp.477-498, 1997.
DOI : 10.1016/S0021-7824(97)89959-X

J. Joly, G. Métivier, and J. Rauch, Generic Rigorous Asymptotic Expansions for Weakly Nonlinear Multidimensional Oscillatory Waves, Duke Mathematical Journal, vol.70, p.373404, 1993.

J. Joly, G. Métivier, and J. Rauch, Coherent and Focusing Multidimensional Nonlinear Geometric Optics, Annales Scientiques de l'ENS Paris, p.51113, 1995.
DOI : 10.24033/asens.1709

URL : http://archive.numdam.org/article/ASENS_1995_4_28_1_51_0.pdf

S. Klainerman and A. Majda, Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids, Communications on Pure and Applied Mathematics, vol.71, issue.4, pp.481-524, 1981.
DOI : 10.1002/cpa.3160340405

H. Koch and D. Tataru, Well-posedness for the Navier???Stokes Equations, Advances in Mathematics, vol.157, issue.1, pp.22-35, 2001.
DOI : 10.1006/aima.2000.1937

J. Leray, Sur le mouvement d'un liquide visqueux emplissant l'espace, Acta Mathematica, vol.63, issue.0, pp.193-248, 1933.
DOI : 10.1007/BF02547354

C. Lucas, Eets de petites échelles, du tenseur des contraintes, des conditions au fond et à la surface sur les équations de Saint-Venant, Thèse de Mathématiques appliquées

A. Mahalov, E. S. Titi, and S. Leibovich, Invariant helical subspaces for the Navier-Stokes equations, Archive for Rational Mechanics and Analysis, vol.190, issue.No. 10, pp.193-222, 1990.
DOI : 10.1007/BF00381234

A. Majda, Compressible uid ow and systems of conservation laws in several space variables

C. Mullaert, Remarks on the equatorial water system, Annales de la Faculté des Sciences de Toulouse, vol.1, pp.27-36, 2011.

C. Mullaert, Study of the non-viscous equatorial shallow water system, Journal de Math??matiques Pures et Appliqu??es, vol.99, issue.3
DOI : 10.1016/j.matpur.2012.09.001

S. Schochet, Fast Singular Limits of Hyperbolic PDEs, Journal of Differential Equations, vol.114, issue.2, pp.476-512, 1994.
DOI : 10.1006/jdeq.1994.1157

M. R. Ukhovskii, V. I. Iudovich, and .. , Axially symmetric flows of ideal and viscous fluids filling the whole space, Journal of Applied Mathematics and Mechanics, vol.32, issue.1, pp.52-61, 1968.
DOI : 10.1016/0021-8928(68)90147-0

R. Ensemble-des-résonances-de and M. , 62 (S ? ) système pénalisé (SL) système limite, pp.31-62