The Vlasov-Poisson dynamics as the mean field limit of extended charges

Abstract

The paper treats the validity problem of the nonrelativistic Vlasov-Poisson equation in $d\ge 2$ dimensions. It is shown that the Vlasov-Poisson dynamics can be derived as a combined mean field and point-particle limit of an N-particle Coulomb system of extended charges. This requires a sufficiently fast convergence of the initial empirical distributions. If the electron radius decreases slower than $N^{-\frac{1}{d(d+2)}}$, the corresponding initial configurations are typical. This result entails propagation of molecular chaos for the respective dynamics

V3: Final version with error corrections, improved exposition

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