The VlasovPoisson Dynamics as the Mean Field Limit of Extended Charges
Abstract
The paper treats the validity problem of the nonrelativistic VlasovPoisson equation in {d ≥ 2} dimensions. It is shown that the VlasovPoisson dynamics can be derived as a combined mean field and pointparticle limit of an Nparticle 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:

Communications in Mathematical Physics
 Pub Date:
 October 2016
 DOI:
 10.1007/s0022001625831
 arXiv:
 arXiv:1502.07047
 Bibcode:
 2016CMaPh.347..271L
 Keywords:

 Mathematical Physics;
 Mathematics  Analysis of PDEs
 EPrint:
 V3: Final version with error corrections, improved exposition