Global existence of classical solutions to the Vlasov-Poisson-Boltzmann system

The time evolution of the distribution function for the charged particles in a dilute gas is governed by the Vlasov-Poisson-Boltzmann system when the force is self-induced and its potential function satisfies the Poisson equation. In this paper, we give a satisfactory global existence theory of classical solutions to this system when the initial data is a small perturbation of a global Maxwellian. Moreover, the convergence rate in time to the global Maxwellian is also obtained through the energy method. The proof is based on the theory of compressible Navier-Stokes equations with forcing and the decomposition of the solutions to the Boltzmann equation with respect to the local Maxwellian introduced in [23] and elaborated in [31].