Classical solvability of the relativistic Vlasov-Maxwell system with bounded spatial density

TL;DR

This paper proves that the relativistic Vlasov-Maxwell system admits a classical solution globally in time under the weaker condition that only the spatial density remains bounded, extending previous results that required bounded kinetic energy density.

Contribution

It demonstrates that bounded spatial density alone suffices for classical solvability, relaxing earlier energy-based conditions.

Findings

Classical solutions exist globally if spatial density is bounded.

Weaker assumptions than previous energy bounds are sufficient.

Extends the understanding of conditions for solvability of the Vlasov-Maxwell system.

Abstract

In (Arch. Rational. Mech. Anal 1986, 92:59-90), Glassey and Strauss showed that if the growth in the momentum of the particles is controlled, then the relativistic Vlasov-Maxwell system has a classical solution globally in time. Later they proved that such control is achieved if the kinetic energy density of the particles remains bounded for all time (Math. Meth. Appl. Sci. 1987, 9:46-52). Here, we show that the latter assumption can be weakened to the boundedness of the spatial density.