In this paper, we study the Cauchy problem for the Boltzmann equation with an external force and the Vlasov-Poisson-Boltzmann system in infinite vacuum. The global existence of solutions is first proved for the Boltzmann equation with an external force which is integrable with respect to time in some sense under the smallness assumption on initial data in weighted norms. For the Vlasov-Poisson-Boltzmann system, the smallness assumption on initial data leads to the decay of the potential field which in turn gives the global existence of solutions by the result on the case with external forces a...
