Derivation of 2D Vlasov-Poisson for classical particles with Coulomb interactions

Abstract

We obtain the first derivation of the 2D Vlasov-Poisson equation for classical particles with Coulomb interactions without any microscopic cutoff. The proof relies on our recent dual hierarchical approach to mean-field limits, together with a refined analysis of dual BBGKY hierarchies on linearized correlations, based on kinetic regularization effects. The result holds more generally for arbitrary singular interaction forces $K\in L_{loc}^{2-\eta }$ with $\eta >0$ small enough, in any dimension, and it extends to Brownian particles. It holds globally in time as long as the mean-field solution is regular enough.

36 pages