HAL - INRIA :: [hal-00609453, version 4] Propagation of chaos for particles approximations of Vlasov equations with singular forces

hal-00609453, version 4

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

Maxime Hauray () ¹, Pierre-Emmanuel Jabin () ^2, 3

(2011)

Résumé : 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.

1 : Laboratoire d'Analyse, Topologie, Probabilités (LATP)
CNRS : UMR6632 – Université de Provence - Aix-Marseille I – Université Paul Cézanne - Aix-Marseille III
2 : TOSCA (INRIA Sophia Antipolis / INRIA Lorraine / IECN)
INRIA – CNRS : UMR7502 – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL)
3 : Laboratoire Jean Alexandre Dieudonné (JAD)
CNRS : UMR6621 – Université de Nice Sophia Antipolis (UNS)

hal-00609453, version 4
http://hal.archives-ouvertes.fr/hal-00609453
oai:hal.archives-ouvertes.fr:hal-00609453
Contributeur : Maxime Hauray <>
Soumis le : Mercredi 22 Février 2012, 11:08:58
Dernière modification le : Mercredi 22 Février 2012, 13:46:27

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arXiv : 1107.3821

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