Global well-posedness of Vlasov-Poisson-type systems in bounded domains

TL;DR

This paper establishes the global existence of classical solutions for Vlasov-Poisson systems within bounded domains, considering specific boundary conditions, advancing the mathematical understanding of these plasma models.

Contribution

It proves the global well-posedness of Vlasov-Poisson systems in bounded domains with boundary conditions, a significant extension of previous unbounded domain results.

Findings

Global existence of classical solutions proven

Specular reflection and Dirichlet/Neumann boundary conditions analyzed

Mathematical framework for bounded domain plasma models developed

Abstract

In this paper we prove global existence of classical solutions to the Vlasov-Poisson and the ionic Vlasov-Poisson models in bounded domains. On the boundary, we consider the specular reflection boundary condition for the Vlasov equation and either homogeneous Dirichlet or Neumann conditions for the Poisson equations.