Solutions of the Vlasov-Maxwell-Boltzmann system with long-range interactions

TL;DR

This paper proves the existence of renormalized solutions for the Vlasov-Maxwell-Boltzmann system with long-range interactions, highlighting the role of entropy dissipation in controlling defect measures crucial for hydrodynamic limits.

Contribution

It introduces a framework for establishing solutions with defect measures in systems with long-range interactions, advancing the mathematical understanding of such kinetic models.

Findings

Existence of renormalized solutions with defect measures.

Control of defect measures via entropy dissipation.

Relevance to hydrodynamic limit analysis.

Abstract

We establish the existence of renormalized solutions of the Vlasov-Maxwell-Boltzmann system with a defect measure in the presence of long-range interactions. We also present a control of the defect measure by the entropy dissipation only, which turns out to be crucial in the study of hydrodynamic limits.