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

TL;DR

This paper proves the global existence and exponential decay of mild solutions to the Vlasov-Maxwell-Fokker-Planck system with small initial data near Maxwellians, extending understanding of kinetic plasma models.

Contribution

It establishes the first global existence and decay results for the Vlasov-Maxwell-Fokker-Planck system with small initial data in a specific function space.

Findings

Global mild solutions exist near Maxwellians.

Solutions decay exponentially over time.

Results extend kinetic plasma theory understanding.

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.