Global Existence of Classical Solutions to the Inelastic Vlasov–Poisson–Boltzmann System

Abstract

We study the global existence and uniqueness of classical solutions to the inelastic Vlasov–Poisson–Boltzmann system for a soft potential in the near vacuum regime. For the global existence of classical solutions, we assume reasonable conditions on the restitution coefficient, which represents the character of inelastic collisions. We use the smallness of initial data and an algebraically decaying weight function in the spatial variable to control the self-consistence force and collision operator.