Mean field propagation of infinite dimensional Wigner measures with a singular two-body interaction potential

We consider the quantum dynamics of many bosons systems in the mean field limit with a singular pair-interaction potential, including the attractive or repulsive Coulombic case in three dimensions. By using a measure transportation technique, we show that Wigner measures propagate along the nonlinear Hartree flow. Such property was previously proved only for bounded potentials in our previous works with a slightly different strategy.