The Plasma-Charge Model: Boundary Effects and Global Well-posedness

TL;DR

This paper investigates the Vlasov-Poisson system with point charges in bounded convex domains, analyzing boundary effects and proving global well-posedness using advanced mathematical techniques.

Contribution

It provides a rigorous characterization of charge-boundary interactions and establishes global well-posedness under various boundary conditions, extending previous work.

Findings

Characterization of charge-boundary effects in convex domains

Proof of global well-posedness for initial-boundary value problems

Development of estimates for Green and Robin functions in convex domains

Abstract

This article focuses on the Vlasov-Poisson system with point charges in bounded convex domains, accounting the interactions of point charges with the self-consistent electric field and the boundary, which were not addressed in the previous work \cite{Wu24}. We provide a rigorous characterization of the charge-boundary effect and establish the global well-posedness of the associated initial-boundary value problems under various boundary conditions. The analysis rests upon delicate estimates of the Green and Robin functions in convex domains, the Pfaffelmoser and Lions-Perthame methods for global well-posedness, and a desingularization argument that justifies the point-charge dynamics.