The Vlasov-Maxwell-Boltzmann/Landau system with polynomial perturbation near Maxwellian

Abstract

In this paper, we study the Vlasov-Maxwell-Boltzmann system without angular cutoff and the Vlasov-Maxwell-Landau/Boltzmann system with polynomial perturbation $F=\mu +f$ near global Maxwellian. In particular, we prove the global existence, uniqueness and large time behavior for solutions in a polynomial weighted space $H_{x,v}^N(⟨v{⟩}^k)$. The method is based on Duhamel's principle with the crucial time-decay analysis on the particle distribution $f$ and the electromagnetic field $(E,B)$.