L. Ambrosio and &. A. Figalli, Geodesics in the Space of Measure-Preserving Maps and Plans, Archive for Rational Mechanics and Analysis, vol.5, issue.5
DOI : 10.1007/s00205-008-0189-2
URL : https://hal.archives-ouvertes.fr/hal-00838835

V. Arnold, Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applicationsàapplications`applicationsà l'hydrodynamique des fluides parfaits, French) Ann. Inst. Fourier (Grenoble), pp.319-361, 1966.
DOI : 10.5802/aif.233
URL : http://archive.numdam.org/article/AIF_1966__16_1_319_0.pdf

Y. Brenier, The least action principle and the related concept of generalized flows for incompressible perfect fluids, Journal of the American Mathematical Society, vol.2, issue.2, pp.225-255, 1989.
DOI : 10.1090/S0894-0347-1989-0969419-8

Y. Brenier, The dual Least Action Problem for an ideal, incompressible fluid, Archive for Rational Mechanics and Analysis, vol.56, issue.4, pp.323-351, 1993.
DOI : 10.1007/BF00375139

Y. Brenier, Homogeneous hydrostatic flows with convex velocity profiles, Nonlinearity, vol.12, issue.3, pp.495-512, 1999.
DOI : 10.1088/0951-7715/12/3/004

Y. Brenier, Minimal geodesics on groups of volume-preserving maps and generalized solutions of the Euler equations, Communications on Pure and Applied Mathematics, vol.111, issue.4, pp.411-452, 1999.
DOI : 10.1002/(SICI)1097-0312(199904)52:4<411::AID-CPA1>3.0.CO;2-3

Y. Brenier, Generalized solutions and hydrostatic approximation of the Euler equations, Physica D: Nonlinear Phenomena, vol.237, issue.14-17, 2008.
DOI : 10.1016/j.physd.2008.02.026

S. Helgason, The Radon Transform, 1980.

A. I. Shnirelman, ON THE GEOMETRY OF THE GROUP OF DIFFEOMORPHISMS AND THE DYNAMICS OF AN IDEAL INCOMPRESSIBLE FLUID, Russian) Mat. Sb. (N.S.), pp.82-109, 1985.
DOI : 10.1070/SM1987v056n01ABEH003025

A. I. Shnirelman, Generalized fluid flows, their approximation and applications, Geometric and Functional Analysis, vol.72, issue.1, pp.586-620, 1994.
DOI : 10.1007/BF01896409