On the uniqueness of probability measure solutions to Liouville's equation of Hamiltonian PDEs.

Quentin Liard (1) , Zied Ammari (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

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.

Mots clés: characteristics theory; wigner measures; continuity equations; Liouville equations

Domaines: Equations aux dérivées partielles [math.AP]

Quentin Liard, Zied Ammari. On the uniqueness of probability measure solutions to Liouville's equation of Hamiltonian PDEs.. 2016. ⟨hal-01275164v2⟩