Abstract
The paper treats the validity problem of the nonrelativistic Vlasov-Poisson equation in \({d \geq 2}\) 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.
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Lazarovici, D. The Vlasov-Poisson Dynamics as the Mean Field Limit of Extended Charges. Commun. Math. Phys. 347, 271–289 (2016). https://doi.org/10.1007/s00220-016-2583-1
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DOI: https://doi.org/10.1007/s00220-016-2583-1