Particles approximations of Vlasov equations with singular forces : Propagation of chaos

@article{Jabin2011ParticlesAO,
title={Particles approximations of Vlasov equations with singular forces : Propagation of chaos},
author={P. Jabin and M. Hauray},
journal={arXiv: Analysis of PDEs},
year={2011}
}

We obtain the mean field limit and the propagation of chaos for a system of particles interacting with a singular interaction force of the type $1/|x|^\alpha$, with $\alpha <1$ in dimension $d \geq 3$. We also provide results for forces with singularity up to $\alpha < d-1$ but with large enough cut-off. This last result thus almost includes the most interesting case of Coulombian or gravitational interaction, but it is also interesting when the strength of the singularity $\alpha$ is larger… Expand