Global Existence of Regular Solutions for the Vlasov–Poisson–Fokker–Planck System

We study the global existence and uniqueness of regular solutions to the Cauchy problem for the Vlasov–Poisson–Fokker–Planck system. Two existence theorems for regular solutions are given under slightly different initial conditions. One of them completely includes the results of P. Degond (1986, Ann. Sci. Ecole Norm. Sup. 19, 519–542).