On Global Existence of Classical Solutions for the Vlasov-Poisson System in Convex Bounded Domains

TL;DR

This paper proves the global existence of strong solutions for the Vlasov-Poisson system within convex bounded domains under specific boundary conditions, advancing understanding in plasma physics modeling.

Contribution

It establishes the first global existence results for classical solutions in convex bounded domains with Dirichlet and specular reflection boundary conditions.

Findings

Global existence of strong solutions proven

Applicable to plasma physics models in bounded domains

Boundary conditions are homogeneous Dirichlet and specular reflection

Abstract

We prove global existence of strong solutions for the Vlasov-Poisson system in a convex bounded domain in the plasma physics case assuming homogeneous Dirichlet boundary conditions for the electric potential and the specular reflection boundary conditions for the distribution density.