Generalized Compressible Flows and Solutions of the $$H(\mathrm {div})$$H(div) Geodesic Problem
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[1] Luca Nenna. Numerical Methods for Multi-Marginal Optimal Transportation , 2016 .
[2] Gabriel Peyré,et al. Iterative Bregman Projections for Regularized Transportation Problems , 2014, SIAM J. Sci. Comput..
[3] L. Ambrosio,et al. Geodesics in the Space of Measure-Preserving Maps and Plans , 2007, math/0701848.
[4] Marco Cuturi,et al. Sinkhorn Distances: Lightspeed Computation of Optimal Transport , 2013, NIPS.
[5] Quentin Mérigot,et al. A Lagrangian Scheme à la Brenier for the Incompressible Euler Equations , 2018, Found. Comput. Math..
[6] G. Peyré,et al. Unbalanced optimal transport: Dynamic and Kantorovich formulations , 2015, Journal of Functional Analysis.
[7] Quentin Mérigot,et al. A Multiscale Approach to Optimal Transport , 2011, Comput. Graph. Forum.
[8] D. Burago,et al. A Course in Metric Geometry , 2001 .
[9] Y. Brenier. The dual Least Action Problem for an ideal, incompressible fluid , 1993 .
[10] Vanishing geodesic distance for right-invariant Sobolev metrics on diffeomorphism groups , 2018, Annals of Global Analysis and Geometry.
[11] Jean-Marie Mirebeau,et al. Minimal Geodesics Along Volume-Preserving Maps, Through Semidiscrete Optimal Transport , 2015, SIAM J. Numer. Anal..
[12] D. Mumford,et al. VANISHING GEODESIC DISTANCE ON SPACES OF SUBMANIFOLDS AND DIFFEOMORPHISMS , 2004, math/0409303.
[13] Jean-David Benamou,et al. Generalized incompressible flows, multi-marginal transport and Sinkhorn algorithm , 2017, Numerische Mathematik.
[14] Alessio Figalli,et al. On the regularity of the pressure field of Brenier’s weak solutions to incompressible Euler equations , 2008 .
[15] Darryl D. Holm,et al. An integrable shallow water equation with peaked solitons. , 1993, Physical review letters.
[16] Darryl D. Holm,et al. The Euler–Poincaré Equations and Semidirect Products with Applications to Continuum Theories , 1998, chao-dyn/9801015.
[17] Y. Brenier. The least action principle and the related concept of generalized flows for incompressible perfect fluids , 1989 .
[18] J. Marsden,et al. Groups of diffeomorphisms and the motion of an incompressible fluid , 1970 .
[19] V. Arnold. Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits , 1966 .
[20] F. Santambrogio. Optimal Transport for Applied Mathematicians: Calculus of Variations, PDEs, and Modeling , 2015 .
[21] François-Xavier Vialard,et al. An Interpolating Distance Between Optimal Transport and Fisher–Rao Metrics , 2010, Foundations of Computational Mathematics.
[22] Global Lagrangian solutions of the Camassa-Holm equation , 2017, 1710.05484.
[23] J. K. Hunter,et al. Dynamics of director fields , 1991 .
[24] Thomas Gallouet,et al. The Camassa-Holm equation as an incompressible Euler equation: a geometric point of view , 2016 .
[25] Simone Di Marino,et al. Metric completion of $Diff([0,1])$ with the $H1$ right-invariant metric , 2019, 1906.09139.
[26] Darryl D. Holm,et al. Wave Structure and Nonlinear Balances in a Family of Evolutionary PDEs , 2002, SIAM J. Appl. Dyn. Syst..
[27] J. Lenells. The Hunter–Saxton equation describes the geodesic flow on a sphere , 2007 .
[28] B. Khesin,et al. Geometry of Diffeomorphism Groups, Complete integrability and Geometric statistics , 2013 .
[29] Giuseppe Savaré,et al. Optimal Entropy-Transport problems and a new Hellinger–Kantorovich distance between positive measures , 2015, 1508.07941.
[30] Athanassios S. Fokas,et al. Symplectic structures, their B?acklund transformation and hereditary symmetries , 1981 .
[31] L. Ambrosio,et al. Gradient Flows: In Metric Spaces and in the Space of Probability Measures , 2005 .
[32] Jerrold E. Marsden,et al. EULER-POINCARE MODELS OF IDEAL FLUIDS WITH NONLINEAR DISPERSION , 1998 .
[33] L. Molinet. On Well-Posedness Results for Camassa-Holm Equation on the Line: A Survey , 2004 .
[34] A. Shnirelman. Generalized fluid flows, their approximation and applications , 1994 .