Global Classical Solutions of the one and one-half dimensional Vlasov-Maxwell Fokker-Planck System

TL;DR

This paper establishes the first global existence and uniqueness results for classical solutions of the one and one-half dimensional Vlasov-Maxwell-Fokker-Planck system, demonstrating improved regularity in the momentum variable.

Contribution

It provides the first proof of well-posedness and regularity gain for solutions to this complex kinetic system.

Findings

Proved global-in-time existence of classical solutions.

Established uniqueness of solutions.

Demonstrated regularity gain in the momentum argument.

Abstract

We study the "one and one-half" dimensional Vlasov-Maxwell-Fokker-Planck system and obtain the first results concerning well-posedness of solutions. Specifically, we prove the global-in-time existence and uniqueness in the large of classical solutions to the Cauchy problem and a gain in regularity of the distribution function in its momentum argument.