The index of elliptic operators, IV. Ann. of Math, vol.93, issue.2, pp.119-138, 1971. ,
Nonlinear analysis on manifolds. Monge-Ampère equations, Grundlehren der Mathematischen Wissenschaften, vol.252 ,
, , 1982.
Smooth perturbations of the functional calculus and applications to riemannian geometry on spaces of metrics, 2018. ,
Fractional Sobolev metrics on spaces of immersed curves, Calc. Var. Partial Differential Equations, vol.57, issue.1, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01486557
Local and Global Well-posedness of the fractional order EPDiff equation on R d, Journal of Differential Equations, vol.258, issue.6, pp.2010-2053, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01111245
Sobolev metrics on shape space of surfaces, J. Geom. Mech, vol.3, issue.4, pp.389-438, 2011. ,
Sobolev metrics on the manifold of all Riemannian metrics, J. Differential Geom, vol.94, issue.2, pp.187-208, 2013. ,
Fractional sobolev metrics on spaces of immersions, 2019. ,
Vanishing distance phenomena and the geometric approach to SQG, Archive for Rational Mechanics and Analysis, 2018. ,
Geometric investigations of a vorticity model equation, J. Differential Equations, vol.260, issue.1, pp.478-516, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01203765
Semi-invariant riemannian metrics in hydrodynamics, 2018. ,
The least action principle and the related concept of generalized flows for incompressible perfect fluids, J. Amer. Math. Soc, vol.2, pp.225-255, 1989. ,
Minimal geodesics on groups of volume-preserving maps and generalized solutions of the Euler equations, Comm. Pure Appl. Math, vol.52, pp.411-452, 1999. ,
Regularity of maps between sobolev spaces, vol.52, pp.11-24, 2017. ,
, The L 2 -metric on C ? (M, N ). arXiv e-prints, 2018.
On completeness of groups of diffeomorphisms, Journal of the European Mathematical Society, vol.19, issue.5, pp.1507-1544, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01253261
An integrable shallow water equation with peaked solitons, Phys. Rev. Lett, vol.71, issue.11, pp.1661-1664, 1993. ,
Équations d'Euler d'un fluide incompressible, Facettes mathématiques de la mécanique des fluides, pp.9-30, 2010. ,
Euler-Poincaré-Arnold equations on semi-direct products II, Discrete Contin. Dyn. Syst, vol.36, issue.11, pp.5993-6022, 2016. ,
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
A simple one-dimensional model for the three-dimensional vorticity equation, Comm. Pure Appl. Math, vol.38, issue.6, pp.715-724, 1985. ,
Formation of strong fronts in the 2-D quasigeostrophic thermal active scalar, Nonlinearity, vol.7, issue.6, p.1495, 1994. ,
The manifold of Riemannian metrics, Global Analysis (Proc. Sympos, vol.XV, pp.11-40, 1968. ,
Groups of diffeomorphisms and the motion of an incompressible fluid, Ann. of Math, vol.92, issue.2, pp.102-163, 1970. ,
Diffeomorphism groups, hydrodynamics and relativity, Proceedings of the Thirteenth Biennial Seminar of the Canadian Mathematical Congress Differential Geometry and Applications, vol.1, pp.135-279, 1971. ,
Partial Differential Equations VI: Elliptic and Parabolic Operators, 1990. ,
Global analysis on open manifolds, 2007. ,
Right-invariant Sobolev metrics of fractional order on the diffeomorphism group of the circle, J. Geom. Mech, vol.6, issue.3, pp.335-372, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-00673137
The geometry of a vorticity model equation, Commun. Pure Appl. Anal, vol.11, issue.4, pp.1407-1419, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00528726
Du mouvement de rotation des corps solides autour d'un axe variable. Mémoires de l'académie des sciences de Berlin, vol.14, pp.154-193, 1765. ,
The basic geometry of the manifold of Riemannian metrics and of its quotient by the diffeomorphism group, Michigan Math. J, vol.36, issue.3, pp.323-344, 1989. ,
Well-posedness of higher dimensional Camassa-Holm equations, Bull. Transilv. Univ. Bra?ov Ser. III, vol.2, issue.51, pp.55-58, 2009. ,
Sobolev spaces on Riemannian manifolds with bounded geometry: general coordinates and traces, Math. Nachr, vol.286, issue.16, pp.1586-1613, 2013. ,
Distributions and operators, Graduate Texts in Mathematics, vol.252, 2009. ,
Momentum maps and measure-valued solutions (peakons, filaments, and sheets) for the EPDiff equation, The breadth of symplectic and Poisson geometry, vol.232, pp.203-235, 2005. ,
The analysis of linear partial differential operators, III. Classics in Mathematics, 2007. ,
On the Regularity of the Composition of Diffeomorphisms, vol.226, 2013. ,
Euler equations on homogeneous spaces and Virasoro orbits, Adv. Math, vol.176, issue.1, pp.116-144, 2003. ,
The super Korteweg-de Vries equation as an Euler equation, Funktsional. Anal. i Prilozhen, vol.21, issue.4, pp.81-82, 1987. ,
The geometry of infinite-dimensional groups, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics, vol.51 ,
, , 2009.
Local well-posedness of the EPDiff equation: a survey, The Journal of Geometric Mechanics, vol.9, issue.2, pp.167-189, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01397112
The Camassa-Holm equation as a geodesic flow on the diffeomorphism group, J. Math. Phys, vol.40, issue.2, pp.857-868, 1999. ,
Families index for Boutet de Monvel operators, Münster J. Math, vol.6, pp.343-364, 2013. ,
On Euler's equation and 'EPDiff, The Journal of Geometric Mechanics, vol.5, issue.3, pp.319-344, 2013. ,
Remarks on infinite-dimensional Lie groups, Relativity, groups and topology, pp.1007-1057, 1983. ,
A shallow water equation as a geodesic flow on the Bott-Virasoro group, J. Geom. Phys, vol.24, issue.3, pp.203-208, 1998. ,
Fredholm properties of Riemannian exponential maps on diffeomorphism groups, Invent. Math, vol.179, issue.1, pp.191-227, 2010. ,
Generalized hunter-saxton equations, optimal information transport, and factorization of diffeomorphisms, The Journal of Geometric Analysis, vol.25, issue.2, pp.1306-1334, 2014. ,
On the group of diffeomorphisms on a compact manifold, Global Analysis (Proc. Sympos, vol.XV, pp.167-183, 1968. ,
Translated from the 1979 Japanese original and revised by the author, Translations of Mathematical Monographs. American Mathematical Society, vol.158, 1997. ,
Pseudo-differential operators and symmetries, Pseudo-Differential Operators. Theory and Applications, vol.2, 2010. ,
Geometry and curvature of diffeomorphism groups with H 1 metric and mean hydrodynamics, J. Funct. Anal, vol.160, issue.1, pp.337-365, 1998. ,
Analysis on groups of diffeomorphisms of manifolds with boundary and the averaged motion of a fluid, J. Differential Geom, vol.55, issue.1, pp.145-191, 2000. ,
Generalized fluid flows, their approximation and applications, Geometric and Functional Analysis, vol.4, pp.586-620, 1994. ,
The geometry of the group of diffeomorphisms and the dynamics of an ideal incompressible fluid. Mat. Sb, vol.144, pp.82-109, 1985. ,
Generalized Euler-Poincaré equations on Lie groups and homogeneous spaces, orbit invariants and applications, Lett. Math. Phys, vol.97, issue.1, pp.45-60, 2011. ,
Theory of Function Spaces II, 1992. ,
Local geometry of deformable templates, SIAM J. Math. Anal, vol.37, issue.1, pp.17-59, 2005. ,
The SQG equation as a geodesic equation, Arch. Ration. Mech. Anal, vol.222, issue.3, pp.1269-1284, 2016. ,
On the geodesic flow on the group of diffeomorphisms of the circle with a fractional Sobolev right-invariant metric, J. Nonlinear Math. Phys, vol.17, issue.1, pp.7-11, 2010. ,