6 citations · 13 across the 10 of their papers we have counts for
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Multiphasic formulation of Vlasov equations and applications
Aymeric Baradat, Lucas Ertzbischoff, Daniel Han-Kwan
This work is a mathematical study of the multiphasic formulation of the Vlasov equation, which consists in recasting this collisionless kinetic equation as a system of coupled pres…
A convergence rate for the entropic JKO scheme
Aymeric Baradat, Sofiane Cherf
The so-called JKO scheme, named after Jordan, Kinderlehrer and Otto, provides a variational way to construct discrete time approximations of certain partial differential equations…
Using Sinkhorn in the JKO scheme adds linear diffusion
Aymeric Baradat, Anastasiia Hraivoronska, Filippo Santambrogio
The JKO scheme is a time-discrete scheme of implicit Euler type that allows to construct weak solutions of evolution PDEs which have a Wasserstein gradient structure. The purpose o…
Nonlinear instability in Vlasov type equations around rough velocity profiles
Aymeric Baradat
In the Vlasov-Poisson equation, every configuration which is homogeneous in space provides a stationary solution. Penrose gave in 1960 a criterion for such a configuration to be li…
Small noise limit and convexity for generalized incompressible flows, Schrödinger problems, and optimal transport
Aymeric Baradat, Léonard Monsaingeon
This paper is concerned with six variational problems and their mutual connections: The quadratic Monge-Kantorovich optimal transport, the Schrödinger problem, Brenier's relaxed mo…
On the existence of a scalar pressure field in the Brödinger problem
Aymeric Baradat
This work deals with the entropic regularization of the Brenier problem for perfect incompressible fluids introduced by Arnaudon, Cruzeiro, Léonard and Zambrini. We show that as in…
Continuous dependence of the pressure field with respect to endpoints for ideal incompressible fluids
Aymeric Baradat
In the Brenier variational model for perfect fluids, the datum is the joint law of the initial and final positions of the particles. In this paper, we show that both the optimal ac…