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

AbstractThis 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