  We prove a global existence result with initial data of low regularity, and
prove the trend to the equilibrium for the Vlasov-Poisson-Fokker-Planck system
with small non linear term but with a possibly large exterior confining
potential in dimension $d=2$ and $d=3$. The proof relies on a fixed point
argument using sharp estimates (at short and long time scales) of the
semi-group associated to the Fokker-Planck operator, which were obtained by the
first author.
