The Vlasov–Poisson–Boltzmann system with angular cutoff for soft potentials

Abstract

This paper is concerned with the Cauchy problem of the Vlasov–Poisson–Boltzmann system near a given global Maxwellian with angular cutoff for a class of soft potentials in three space dimensions and the main purpose here is to derive the global solvability of such a problem without the neutral condition which was imposed in Duan et al. (2013) [11] on the initial perturbation. Our analysis is based on a time-weighted energy method and some delicate estimates on its solutions which show that the L2(Rx3×Rξ3)-norms of the solutions with higher order x-derivatives enjoy sharper time-decay rates.