On the Vlasov-Poisson-Fokker-Planck equation near Maxwellian
  We establish the exponential time decay rate of smooth solutions of small amplitude to the Vlasov-Poisson-Fokker-Planck equations to the Maxwellian both in the whole space and in the periodic box via the uniform-in-time energy estimates and also the macroscopic equations. 
Hyung Ju Hwang and Juhi Jang
math.AP