On the mean-field limit for the Vlasov-Poisson system in two dimensions

2025/09/22 by Manuela Feistl-Held, Feistl-Held, Manuela, Peter Pickl +1
Mathematics · Economics, Econometrics and Finance · #Gas Dynamics and Kinetic Theory #Stochastic processes and financial applications #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2509.17821

Abstract

We present a probabilistic proof of the mean-field limit and propagation of chaos of a classical N-particle system in two dimensions with Coulomb interaction force of the form f^N(q)=±(q)/(|q|²) and N-dependent cut-off at |q|>N^-2. In particular, for typical initial data, we show convergence of the Newtonian trajectories to the characteristics of the Vlasov-Poisson system. The proof is based on a Gronwall estimate for the maximal distance between the exact microscopic dynamics and the approximate mean-field dynamics. Thus our result leads to a derivation of the Vlasov-Poisson equation from the microscopic N-particle dynamics with force term arbitrary close to the physically relevant Coulomb force.

Citations

• Quasineutral limit for Vlasov-Poisson with Penrose stable data
• A mean field limit for the Vlasov-Poisson system
• Quasineutral limit of the Vlasov-Poisson system with massless electrons
• N particles approximation of the Vlasov equations with singular potential

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