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

Pierre-Emmanuel Jabin 1, 2 Maxime Hauray 3
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.
Document type :
Journal articles
Liste complète des métadonnées

Cited literature [39 references]  Display  Hide  Download

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

Files

VlaWass-N+7.pdf
Files produced by the author(s)

Licence


Distributed under a Creative Commons Attribution - NonCommercial - NoDerivatives 4.0 International License

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⟩

Share

Metrics

Record views

1400

Files downloads

136