Section: New Results

Generalized incompressible flows, multi-marginal transport and Sinkhorn algorithm

J-D. Benamou, G. Carlier, L. Nenna

Starting from Brenier's relaxed formulation of the incompress-ible Euler equation in terms of geodesics in the group of measure-preserving diffeomorphisms, we propose in [27] a numerical method based on Sinkhorn's algorithm for the entropic regularization of optimal transport. We also make a detailed comparison of this entropic regular-ization with the so-called Bredinger entropic interpolation problem (see [1]). Numerical results in dimension one and two illustrate the feasibility of the method.