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 ≥ 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^{-{1/d(d+2)}}}, the corresponding initial configurations are typical. This result entails propagation of molecular chaos for the respective dynamics.
- Publication:
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Communications in Mathematical Physics
- Pub Date:
- October 2016
- DOI:
- 10.1007/s00220-016-2583-1
- arXiv:
- arXiv:1502.07047
- Bibcode:
- 2016CMaPh.347..271L
- Keywords:
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- Mathematical Physics;
- Mathematics - Analysis of PDEs
- E-Print:
- V3: Final version with error corrections, improved exposition