On classical solutions to the 3D relativistic Vlasov-Maxwell system: Glassey-Strauss' theorem revisited

TL;DR

This paper revisits and simplifies Glassey and Strauss's 1986 proof that classical solutions to the 3D relativistic Vlasov-Maxwell system remain regular as long as the momentum support stays bounded.

Contribution

The paper provides a simplified proof of a key theorem ensuring the global regularity of solutions to the 3D relativistic Vlasov-Maxwell system.

Findings

Classical solutions do not develop singularities if momentum support remains bounded.

Simplified proof enhances understanding of the conditions for solution regularity.

Revisits foundational results in relativistic plasma physics.

Abstract

R. Glassey and W. Strauss have proved in [Arch. Rational Mech. Anal. 92 (1986), 59--90] that classical solutions to the relativistic Vlasov-Maxwell system in three space dimensions do not develop singularities as long as the support of the distribution function in the momentum variable remains bounded. The present paper simplifies their proof.