Global classical solutions of the Vlasov-Darwin system for small initial data

TL;DR

This paper proves the global existence of classical solutions for the Vlasov-Darwin system with small initial data and shows that spherical symmetry reduces it to the relativistic Vlasov-Poisson system.

Contribution

It establishes the first global-in-time existence result for the Vlasov-Darwin system under small initial data and links spherical symmetry to the relativistic Vlasov-Poisson system.

Findings

Global classical solutions exist for small initial data.

Spherical symmetry reduces the system to the relativistic Vlasov-Poisson system.

The system degenerates under symmetry assumptions.

Abstract

A global-in-time existence theorem for classical solutions of the Vlasow-Darwin system is given under the assumption of smallness of the initial data. Furthermore it is shown that in case of spherical symmetry the system degenerates to the relativistic Vlasov-Poisson system.