The Vlasov-Poisson-Boltzmann system in the whole space : The hard potential case

This paper is concerned with the Cauchy problem on the Vlasov-Poisson-Boltzmann system for hard potentials in the whole space. When the initial data is a small perturbation of a global Maxwellian, a satisfactory global existence theory of classical solutions to this problem, together with the corresponding temporal decay estimates on the global solutions, is established. Our analysis is based on time-decay properties of solutions and a new time-velocity weight function which is designed to control the large-velocity growth in the nonlinear term for the case of non-hard-sphere interactions. © 2012 Elsevier Inc.