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

1 TOSCA
INRIA Lorraine, CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, INPL - Institut National Polytechnique de Lorraine, CNRS - Centre National de la Recherche Scientifique : UMR7502
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 $1/|x|^\alpha$, 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 but close to one, in which case it allows for very small cut-off.
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Journal articles

Cited literature [39 references]

https://hal.archives-ouvertes.fr/hal-00609453
Contributor : Maxime Hauray <>
Submitted on : Wednesday, May 8, 2013 - 10:36:29 PM
Last modification on : Monday, March 4, 2019 - 2:04:18 PM
Document(s) archivé(s) le : Tuesday, April 4, 2017 - 6:08:40 AM

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### Identifiers

• HAL Id : hal-00609453, version 5
• ARXIV : 1107.3821

### Citation

Pierre-Emmanuel Jabin, Maxime Hauray. Particles approximations of Vlasov equations with singular forces : Propagation of chaos.. Annales Scientifiques de l'École Normale Supérieure, Elsevier Masson, 2015. ⟨hal-00609453v5⟩

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