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arXiv · 1107.3821

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

Pierre-Emmanuel Jabin·Maxime Hauray
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Abstract

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 $1/|x|^α$, with $α<1$ in dimension $d \geq 3$. We also provide results for forces with singularity up to $α< d-1$ 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 $α$ is larger but close to one, in which case it allows for very small cut-off.

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Pierre-Emmanuel Jabin, Maxime Hauray. 2014-03-31. Particles approximations of Vlasov equations with singular forces : Propagation of chaos. https://arxiv.org/abs/1107.3821

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