On Global Existence of Classical Solutions for the Vlasov-Poisson System   in Convex Bounded Domains
  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. 
Hyung Ju Hwang, Jaewoo Jung, Juan J. L. Velazquez
math.AP