Global mild solutions to the Vlasov-Maxwell-Fokker-Planck system

Abstract

Motivated by Duan et al.[Global Mild Solutions of the Landau and Non-Cutoff Boltzmann Equations, Comm. Pure Appl. Math., 74(5), 932-1020.], the global existence of mild solutions to the Vlasov-Maxwell-Fokker-Planck system near a global Maxwellians with small-amplitude initial data in the function space $L^1_kL^\infty_TL^2_v$ is constructed. Moreover, the exponential time decay of the solutions is obtained.