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

Zied Ammari (1) , Quentin Liard (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: Liouville equations; characteristics theory; wigner measures; continuity equations

Domaines: Equations aux dérivées partielles [math.AP]

Zied Ammari, Quentin Liard. On the uniqueness of probability measure solutions to Liouville's equation of Hamiltonian PDEs.. Discrete and Continuous Dynamical Systems - Series A, 2018, 38 (2), pp.723-748. ⟨10.3934/dcds.2018032⟩. ⟨hal-01275164v3⟩