Section: New Results

Generalized incompressible flows, multi-marginal transport and Sinkhorn algorithm

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

[24]

Starting from Brenier's relaxed formulation of the incompressible Euler equation in terms of geodesics in the group of measurepreserving diffeomorphisms, we propose a numerical method based on Sinkhorn?s algorithm for the entropic regularization of optimal transport. We also make a detailed comparison of this entropic regularization with the so-called Bredinger entropic interpolation problem. Numerical results in dimension one and two illustrate the feasibility of the method.