The Boltzmann equation with frictional force for soft potentials in the whole space

This paper is concerned with the Cauchy problem of the Boltzmann equation with frictional force for both cutoff and non-cutoff soft potentials in the whole space and our main purpose is to establish its global solvability result near a given global Maxwellian and to deduce the temporal convergence rates of such a global solution toward the global Maxwellian when initial perturbation is sufficiently small. The analysis is based on the time-weighted energy method building also upon the recent studies of the cutoff Vlasov–Poisson–Boltzmann system [14] and [15], the non-cutoff Vlasov–Poisson–Boltzmann system [8], and non-cutoff Vlasov–Maxwell–Boltzmann system [9].