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In view of studying incompressible inviscid fluids, Brenier introduced in the late 80's a relaxation of a geodesic problem addressed by Arnold in 1966.
Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l’hydrodynamique des fluides parfaits
V. Arnold · 1966
Earlier work this paper cites.
Dynamical theories of Brownian motion
E. Nelson · 1967
Earlier work this paper cites.
Groups of diffeomorphisms and the motion of an incompressible fluid
D. Ebin and J. Marsden · 1970
Earlier work this paper cites.
A variational principle for the Navier-Stokes equation
K. Yasue · 1983
Earlier work this paper cites.
The geometry of the group of diffeomorphisms and the dynamics of an ideal incompressible fluid
A.I. Shnirelman · 1985
Earlier work this paper cites.
Random fields and diffusion processes, in École d’été de Probabilités de Saint-Flour XV-XVII-1985-87
H. Föllmer · 1988
Earlier work this paper cites.
A combinatorial algorithm for the Euler equations of incompressible flows
Y. Brenier · 1989
Earlier work this paper cites.
The least action principle and the related concept of generalized flows for incompressible perfect fluids
Y. Brenier · 1989
Cited alongside, same era.
The dual least action problem for an ideal, incompressible fluid
Y. Brenier · 1993
Cited alongside, same era.
Generalized fluid flows, their approximation and applications
A.I. Shnirelman · 1994
Cited alongside, same era.
A homogenized model for vortex sheets
Y. Brenier · 1997
Cited alongside, same era.
Entropy minimization and Schrödinger processes in infinite dimensions
H. Föllmer and N. Gantert · 1997
Cited alongside, same era.
Minimal geodesics on groups of measure-preserving maps and generalized solutions of the Euler equations
Y. Brenier · 1999
Cited alongside, same era.
Geodesics in the space of measure-preserving maps and plans
L. Ambrosio and A. Figalli · 2009
Later among the works it cites.
Transport inequalities. A survey
N. Gozlan and C. Léonard · 2010
Later among the works it cites.
From the Schrödinger problem to the Monge-Kantorovich problem
C. Léonard · 2012
Later among the works it cites.
Girsanov theory under a finite entropy condition
C. Léonard · 2012
Later among the works it cites.
Generalized stochastic flows and applications to incompressible viscous fluids
A. Antoniouk, M. Arnaudon, and A.B. Cruzeiro · 2014
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Some properties of path measures
C. Léonard · 2014
Later among the works it cites.
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On the regularity of the pressure field of Brenier’s weak solutions to incompressible Euler equations
L. Ambrosio and A. Figalli · 2008
Cited alongside, same era.
Generalized stochastic lagrangian paths for the Navier-Stokes equation
M. Arnaudon, A.B. Cruzeiro, and S. Fang
Cited in the paper.
Minimizing the relative entropy with respect to Markov and reciprocal measures
A. Baradat and C. Léonard
Cited in the paper.
Lecture notes on convex optimization with some applications to probability theory
C. Léonard
Cited in the paper.
A survey of the Schrödinger problem and some of its connections with optimal transport
C. Léonard · 2014
Later among the works it cites.