The Vlasov-Poisson-Fokker-Planck system with infinite kinetic energy

We build solutions to the three dimensional Vlasov-Poisson-Fokker-Planck System having infinite kinetic energy. For that purpose, we first derive a new conservation law, which states the propagation of the second space moment for solutions to this system. The existence of such infinite kinetic energy solutions relies essentialy on the dispersive effects of the kinetic transport. We also show strong regularizing effects, such as an L-x(infinity) bound on the farce field, combining dispersive properties and smoothing effects of the diffusion.