Global Existence for the "One and one-half" dimensional relativistic Vlasov-Maxwell-Fokker-Planck system

TL;DR

This paper proves the global existence and uniqueness of classical solutions for a relativistic Vlasov-Maxwell-Fokker-Planck system in one and one-half dimensions, advancing understanding of relativistic particle dynamics with electromagnetic interactions.

Contribution

It introduces the first well-posedness results for the relativistic Vlasov-Maxwell-Fokker-Planck system in this setting, including regularity improvements.

Findings

Global-in-time existence of solutions

Uniqueness of classical solutions

Regularity gain in the distribution function

Abstract

In a recent paper Calogero and Alcantara derived a Lorentz-invariant Fokker-Planck equation, which corresponds to the evolution of a particle distribution associated with relativistic Brownian Motion. We study the "one and one-half" dimensional version of this problem with nonlinear electromagnetic interactions - the relativistic 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 of classical solutions to the Cauchy problem and a gain in regularity of the distribution function in its momentum argument.