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

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 $L_x^2$.

24 pages