Propagation of chaos for particles approximations of Vlasov equations with singular forces

Details Propagation of chaos for particles approximations of Vlasov equations with singular forces Propagation of chaos for particles approximations of Vlasov equations with singular forces

2011-07-19

arxiv.org/abs/1107.3821v4

Mathematics

Analysis of PDEs

Scientific paper

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 provides 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 gravitationnal interaction.

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