M. Bruveris and F. Vialard, On completeness of groups of diffeomorphisms, J. Eur. Math. Soc. (JEMS), vol.19, issue.5, pp.1507-1544, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01253261

R. Camassa and D. D. Holm, An integrable shallow water equation with peaked solitons, Phys. Rev. Lett, vol.71, issue.11, pp.1661-1664, 1993.
DOI : 10.1103/physrevlett.71.1661

A. Constantin and B. Kolev, Geodesic flow on the diffeomorphism group of the circle, Comment. Math. Helv, vol.78, issue.4, pp.787-804, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00003261

G. Crippa and C. De-lellis, Estimates and regularity results for the diperna-lions flows, J. REINE ANGEW. MATH, pp.15-46, 2008.
DOI : 10.1515/crelle.2008.016
URL : http://doc.rero.ch/record/302948/files/crelle.2008.016.pdf

G. David, J. Ebin, and . Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid, Ann. of Math, vol.92, issue.2, pp.102-163, 1970.

N. Falkner and G. Teschl, On the substitution rule for lebesgue-stieltjes integrals, Expositiones Mathematicae, vol.30, issue.4, pp.412-418, 2012.
DOI : 10.1016/j.exmath.2012.09.002
URL : https://doi.org/10.1016/j.exmath.2012.09.002

T. Gallouët, A. Natale, and F. Vialard, Generalized compressible fluid flows and solutions of the Camassa-Holm variational model. arXiv e-prints, 2018.

T. Gallouët and F. Vialard, The camassa-holm equation as an incompressible euler equation: A geometric point of view, Journal of Differential Equations, 2017.

W. Peter, D. Michor, and . Mumford, Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms, Doc. Math, vol.10, pp.217-245, 2005.

X. François, A. Vialard, and . Natale, INdAM E-mail address: simone.dimarino@altamatematica.it INRIA, 2018.

, E-mail address: fxvialard@normalesup.org