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 $σ_{-1}(t, x) = \max_{|ω|=1} \,\int_{R^3} \frac{dp}{\sqrt{1+p^2}}\, \frac{1}{(1+v\cdotω)}\, f(t, x, p)$ is bounded in $L^2_x$.

24 pages