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

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.