Global mild solutions to the relativistic Vlasov–Poisson–Fokker–Planck system in the whole space

Abstract

In this manuscript, we consider the Cauchy problem of the relativistic Vlasov–Poisson–Fokker–Planck system in the whole space. The global existence and the exponential time decay rates of the mild solutions around a global relativistic Maxwellian are obtained under assumption that initial data satisfies some smallness in the low regularity space Lk1LT∞Lv2.