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arXiv · 2608.04104

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

Mitia Duerinckx·Pierre-Emmanuel Jabin
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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 $K\in L^{2-\eta}_{loc}$ 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.

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Mitia Duerinckx, Pierre-Emmanuel Jabin. 2026-08-04. Derivation of 2D Vlasov-Poisson for classical particles with Coulomb interactions. https://arxiv.org/abs/2608.04104

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