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A Mean Field Limit for the Vlasov–Poisson System

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Abstract

We present a probabilistic proof of the mean field limit and propagation of chaos N-particle systems in three dimensions with positive (Coulomb) or negative (Newton) 1/r potentials scaling like 1/N and an N-dependent cut-off which scales like \({N^{-1/3+ \epsilon}}\). In particular, for typical initial data, we show convergence of the empirical distributions to solutions of the Vlasov–Poisson system with either repulsive electrical or attractive gravitational interactions.

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Authors and Affiliations

  1. Mathematisches Institut, Ludwig-Maximilians Universität, Theresienstr. 39, 80333, Munich, Germany

    Dustin Lazarovici & Peter Pickl

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  1. Dustin Lazarovici
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  2. Peter Pickl
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Correspondence to Dustin Lazarovici.

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Communicated by P.-L. Lions

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Lazarovici, D., Pickl, P. A Mean Field Limit for the Vlasov–Poisson System. Arch Rational Mech Anal 225, 1201–1231 (2017). https://doi.org/10.1007/s00205-017-1125-0

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