Yet another criterion for global existence in the 3D relativistic Vlasov-Maxwell system

TL;DR

This paper introduces a new criterion involving a specific integral quantity that guarantees the extension of solutions in the 3D relativistic Vlasov-Maxwell system, advancing understanding of solution longevity.

Contribution

It establishes a novel boundedness condition on a particular integral quantity that ensures global existence of solutions in the relativistic Vlasov-Maxwell system.

Findings

Solutions extend as long as the integral quantity σ_{-1} remains bounded in L^2_x.

Provides a new criterion for global existence in the relativistic Vlasov-Maxwell system.

Enhances understanding of conditions preventing finite-time blow-up.

Abstract

We prove that solutions of the 3D relativistic Vlasov-Maxwell system can be extended, as long as the quantity $\sigma_{-1}(t, x) = \max_{|\omega|=1} \,\int_{R^3} \frac{dp}{\sqrt{1+p^2}}\, \frac{1}{(1+v\cdot\omega)}\, f(t, x, p)$ is bounded in $L^2_x$.