Momentum Regularity and Stability of the Relativistic Vlasov-Maxwell-Boltzmann System

TL;DR

This paper proves momentum regularity and stability for the relativistic Vlasov-Maxwell-Boltzmann system, establishing global existence of classical solutions near Maxwellian in a periodic setting through novel splitting techniques.

Contribution

It introduces a new splitting method and frame interplay to establish momentum regularity and prove global solutions for the relativistic Vlasov-Maxwell-Boltzmann system.

Findings

Momentum regularity established in energy spaces.

Global existence of classical solutions near Maxwellian.

New splitting technique improves analysis of relativistic collision operator.

Abstract

In the study of solutions to the relativistic Boltzmann equation, their regularity with respect to the momentum variables has been an outstanding question, even local in time, due to the initially unexpected growth in the post-collisional momentum variables which was discovered in 1991 by Glassey & Strauss \cite{MR1105532}. We establish momentum regularity within energy spaces via a new splitting technique and interplay between the Glassey-Strauss frame and the center of mass frame of the relativistic collision operator. In a periodic box, these new momentum regularity estimates lead to a proof of global existence of classical solutions to the two-species relativistic Vlasov-Boltzmann-Maxwell system for charged particles near Maxwellian with hard ball interaction.