The Vlasov–Maxwell–Fokker–Planck system near Maxwellians in ℝ3

Abstract

ABSTRACT Motivated by Duan and Strain [Optimal large-time behavior of the Vlasov–Maxwell–Boltzmann system in the whole space. Comm Pure Appl Math. 2011;64:1497–1546], we prove the global existence of solutions to the Vlasov–Maxwell–Fokker–Planck system near Maxwellians in the whole space by utilizing the refined energy method. In the proof of the global existence, the a priori estimates on the macroscopic component and the electromagnetic field are obtained by use of the macroscopic balance laws and the Maxwell equations, respectively. Moreover, the optimal time decay of solutions to the global Maxwellians, which can be obtained by employing the Fourier analysis.