PROJECTIONS ONTO THE CONE OF OPTIMAL TRANSPORT MAPS AND COMPRESSIBLE FLUID FLOWS

Abstract

The system of isentropic Euler equations in the potential flow regime can be considered formally as a second order ordinary differential equation on the Wasserstein space of probability measures. This interpretation can be used to derive a variational time discretization. We prove that the approximate solutions generated by this discretization converge to a measure-valued solution of the isentropic Euler equations. The key ingredient is a characterization of the polar cone to the cone of optimal transport maps.