The mean field limit for the Vlasov–Poisson system with a point charge

In this paper, we are concerned with the validity problem for the repulsive Vlasov–Poisson system when the initial datum is the sum of a diffuse density and a point charge in the three dimensional space. Our result leads to a derivation of this system from the regularized microscopic N-plasma particle and one point charge system when the Coulomb force between plasma particles needs to be modified with the modified size N−13+ϵ while the Coulomb force between plasma and point charge does not need to be modified. More precisely, we obtain the convergence rate between the empirical measure associated to the regularized particle system and the solution of the Vlasov–Poisson system with a point charge in terms of the Wasserstein distance.