On the uniqueness of probability measure solutions to Liouville's equation of Hamiltonian PDEs
arXiv:1602.06716
Abstract
In this paper, we give a uniqueness result to a transport equation fulfilled by probability measure on a infinite dimensional Hilbert space. Main arguments are based on projective aspects and a probabilistic representation of the solutions. It extends the work of Maniglia, which concerns the finite dimensional case and the work of Ammari and Nier, for a wider class of velocity field.
version 3, 2016-14