Global L1 theory and regularity for the 3D nonlinear Wigner–Poisson–Fokker–Planck system

A global existence, uniqueness and regularity theorem is proved for the simplest Markovian Wigner–Poisson– Fokker–Planck model incorporating friction and dissipation mechanisms. The proof relies on Green function and energy estimates under mild formulation, making essential use of the Husimi function and the elliptic regularization of the Fokker–Planck operator.