A. Castro and D. Córdoba, Infinite energy solutions of the surface quasi-geostrophic equation, Advances in Mathematics, vol.225, issue.4, pp.1820-1829, 2010.
DOI : 10.1016/j.aim.2010.04.018

A. Constantin and B. Kolev, On the geometric approach to the motion of inertial mechanical systems, Journal of Physics A: Mathematical and General, vol.35, issue.32, pp.51-79, 2002.
DOI : 10.1088/0305-4470/35/32/201

URL : https://hal.archives-ouvertes.fr/hal-00003269

A. Constantin and B. Kolev, Geodesic flow on the diffeomorphism group of the circle, Commentarii Mathematici Helvetici, vol.78, issue.4, pp.787-804, 2003.
DOI : 10.1007/s00014-003-0785-6

URL : https://hal.archives-ouvertes.fr/hal-00003261

P. Constantin, P. D. Lax, and A. Majda, A simple one-dimensional model for the three-dimensional vorticity equation, Communications on Pure and Applied Mathematics, vol.44, issue.6, pp.715-724, 1985.
DOI : 10.1002/cpa.3160380605

A. Córdoba, D. Córdoba, and M. A. Fontelos, Formation of singularities for a transport equation with nonlocal velocity, Ann. of Math, issue.23, pp.1621377-1389, 2005.

A. Córdoba, D. Córdoba, and M. A. Fontelos, Integral inequalities for the Hilbert transform applied to a nonlocal transport equation, Journal de Math??matiques Pures et Appliqu??es, vol.86, issue.6, pp.529-540, 2006.
DOI : 10.1016/j.matpur.2006.08.002

S. Gregorio, On a one-dimensional model for the three-dimensional vorticity equation, Journal of Statistical Physics, vol.157, issue.5-6, pp.5-61251, 1990.
DOI : 10.1007/BF01334750

C. De-lellis, T. Kappeler, and P. Topalov, Low-Regularity Solutions of the Periodic Camassa???Holm Equation, Communications in Partial Differential Equations, vol.21, issue.1, pp.87-126, 2007.
DOI : 10.1002/1097-0312(200011)53:11<1411::AID-CPA4>3.0.CO;2-5

N. Dunford, J. T. Schwartz-william, G. Bade, and R. G. Bartle, Linear operators. Part I. Wiley Classics Library General theory, 1988.

D. G. Ebin and J. Marsden, Groups of Diffeomorphisms and the Motion of an Incompressible Fluid, The Annals of Mathematics, vol.92, issue.1, pp.102-163, 1970.
DOI : 10.2307/1970699

J. Escher and B. Kolev, The Degasperis???Procesi equation as a non-metric Euler equation, Mathematische Zeitschrift, vol.46, issue.3, pp.1-17, 2010.
DOI : 10.1007/s00209-010-0778-2

URL : https://hal.archives-ouvertes.fr/hal-00409022

J. Escher and J. Seiler, The periodic b-equation and Euler equations on the circle, Journal of Mathematical Physics, vol.51, issue.5, 2010.
DOI : 10.1063/1.3405494

J. Escher and M. Wunsch, Restrictions on the geometry of the periodic vorticity equation. ArXiv e-prints, 2010.

L. Euler, Principes généraux du mouvement des fluides. Mémoires de l'académie des sciences de Berlin, pp.274-315

F. Gay-balmaz, Infinite dimensional geodesic flows and the universal Teichmüller space, 2009.

L. Guieu, C. Roger, . Et-le-groupe-de, and . Virasoro, Aspects géométriques et algébriques, généralisations. [Geometric and algebraic aspects, 2007.

R. S. Hamilton, The inverse function theorem of Nash and Moser, Bulletin of the American Mathematical Society, vol.7, issue.1, pp.65-222, 1982.
DOI : 10.1090/S0273-0979-1982-15004-2

B. Khesin and G. Misio-lek, Euler equations on homogeneous spaces and Virasoro orbits, Advances in Mathematics, vol.176, issue.1, pp.116-144, 2003.
DOI : 10.1016/S0001-8708(02)00063-4

B. Kolev, Some geometric investigations on the Degasperis???Procesi shallow water equation, Wave Motion, vol.46, issue.6, pp.412-419, 2009.
DOI : 10.1016/j.wavemoti.2009.06.005

URL : https://hal.archives-ouvertes.fr/hal-00418525

J. Lenells, The Hunter???Saxton equation describes the geodesic flow on a sphere, Journal of Geometry and Physics, vol.57, issue.10, pp.2049-2064, 2007.
DOI : 10.1016/j.geomphys.2007.05.003

J. Lenells, The Hunter???Saxton Equation: A Geometric Approach, SIAM Journal on Mathematical Analysis, vol.40, issue.1, pp.266-277, 2008.
DOI : 10.1137/050647451

H. Okamoto, T. Sakajo, and M. Wunsch, On a generalization of the Constantin???Lax???Majda equation, Nonlinearity, vol.21, issue.10, pp.2447-2461, 2008.
DOI : 10.1088/0951-7715/21/10/013

J. N. Pandey, The Hilbert transform of Schwartz distributions and applications, Pure and Applied Mathematics, 1996.
DOI : 10.1002/9781118032510

T. Sakajo, Blow-up solutions of the Constantin-Lax-Majda equation with a generalized viscosity term, J. Math. Sci. Univ. Tokyo, vol.10, issue.1, pp.187-207, 2003.

T. Sakajo, On global solutions for the Constantin???Lax???Majda equation with a generalized viscosity term, Nonlinearity, vol.16, issue.4, pp.1319-1328, 2003.
DOI : 10.1088/0951-7715/16/4/307

S. Schochet, Explicit solutions of the viscous model vorticity equation, Communications on Pure and Applied Mathematics, vol.31, issue.4, pp.531-537, 1986.
DOI : 10.1002/cpa.3160390404

L. A. Takhtajan and L. Teo, Weil-Petersson metric on the universal Teichmüller space, Mem. Amer. Math. Soc, vol.183, issue.861, p.119, 2006.

F. T??-glay and C. Vizman, Generalized Euler-Poincaré equations on Lie groups and homogeneous spaces, orbit invariants and applications. ArXiv e-prints: 1008, 2010.

E. Wegert and A. S. Vasudeva-murthy, Blow-Up in a Modified Constantin-Lax-Majda Model for the Vorticity Equation, Zeitschrift f??r Analysis und ihre Anwendungen, vol.18, issue.2, pp.183-191, 1999.
DOI : 10.4171/ZAA/876

M. Wunsch, ON THE GEODESIC FLOW ON THE GROUP OF DIFFEOMORPHISMS OF THE CIRCLE WITH A FRACTIONAL SOBOLEV RIGHT-INVARIANT METRIC, Journal of Nonlinear Mathematical Physics, vol.36, issue.1, pp.7-11, 2010.
DOI : 10.1142/S1402925110000544