On a characteristic initial value problem in Plasma physics

TL;DR

This paper studies the relativistic Vlasov-Maxwell system in plasma physics with initial data on a past light cone, exploring solution existence, conservation laws, and symmetry cases within a characteristic initial value framework.

Contribution

It introduces a characteristic initial value problem on a light cone for the Vlasov-Maxwell system and analyzes solution existence and conservation properties, especially in spherical symmetry.

Findings

Mass-energy conservation holds for solutions.

Unique classical solutions exist in spherical symmetry.

Solutions' mass-energy matches on light cones.

Abstract

The relativistic Vlasov-Maxwell system of plasma physics is considered with initial data on a past light cone. This characteristic initial value problem arises in a natural way as a mathematical framework to study the existence of solutions isolated from incoming radiation. Various consequences of the mass-energy conservation and of the absence of incoming radiation condition are first derived assuming the existence of global smooth solutions. In the spherically symmetric case, the existence of a unique classical solution in the future of the initial cone follows by arguments similar to the case of initial data at time $t=0$. The total mass-energy of spherically symmetric solutions equals the (properly defined) mass-energy on backward and forward light cones.