Global weak solutions for the Vlasov–Poisson system with a point charge

We study the dynamics of three‐dimensional Vlasov‐Poisson system in the presence of a point charge with attractive interaction. Compared to the repulsive interaction,we cannot get a priori conversation law. Nevertheless,we are able to obtain bound of kinetic energy by introducing a Lyapunov functional. Combining this result with the concept of Diperna‐Lions flow, we establish global existence of weak solutions for this system.