On the three-dimensional Wigner--Poisson problem with inflow boundary conditions (Q2577153)

The author studies the 3-dimensional Wigner-Poisson problem on a spatially bounded domain with time-dependent inflow boundary conditions, the problem thus being an open quantum system not equivalent to Schroedinger-Poisson. A local-in-time result is proved by introducing a functional setting which allows to treat the problem as in the 1-dimensional case locally, i.e. using a fixed point argument.