Title: On the velocities of flows consisting of cyclically monotone maps

Authors: A. Tudorascu

Issue: Volume 59 (2010), Issue 3, 929-956

Abstract: Motivated by work on one-dimensional Euler-Poisson systems, Gangbo et al. proved a surprisingly general flow-map formula which unequivocally links an absolutely continuous curve in the Wasserstein space to the corresponding family of optimal maps pushing forward a given reference measure to each measure on the curve. In this work we prove a similar result for higher dimensions. Possible applications to variational solutions for pressureless gas dynamics systems are discussed. These solutions are obtained as absolutely continuous curves in a new metric space which is topologically equivalent to the Wasserstein space.