On the energy conservation by weak solutions of the relativistic Vlasov-Maxwell system

TL;DR

This paper proves that under certain regularity conditions, weak solutions to the relativistic Vlasov-Maxwell system conserve total energy, highlighting conditions on electromagnetic fields and particle distributions.

Contribution

It establishes energy conservation for weak solutions of the relativistic Vlasov-Maxwell system under specific bounded variation and integrability conditions.

Findings

Weak solutions preserve total energy under specified conditions.

Electromagnetic fields must be locally of bounded variation.

Particle distribution functions require square integrable moments.

Abstract

We show that weak solutions of the relativistic Vlasov-Maxwell system preserve the total energy provided that the electromagnetic field is locally of bounded variation and, for any $\lambda$> 0, the one-particle distribution function has a square integrable $\lambda$-moment in the momentum variable.