  The Vlasov-Poisson system with massless electrons (VPME) is widely used in
plasma physics to model the evolution of ions in a plasma. It differs from the
Vlasov-Poisson system (VP) for electrons in that the Poisson coupling has an
exponential nonlinearity that creates several mathematical difficulties. In
particular, while global well-posedness in 3D is well understood in the
electron case, this problem remained completely open for the ion model with
massless electrons. The aim of this paper is to fill this gap by proving
uniqueness for VPME in the class of solutions with bounded density, and global
existence of solutions with bounded density for a general class of initial
data, generalising all the previous results known for VP.
