On the uniqueness of probability measure solutions to Liouville's   equation of Hamiltonian PDEs
  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. 
Zied Ammari (IRMAR), Quentin Liard (IRMAR)
math.AP