Abstract
We consider a N-particle system interacting through the Newtonian potential with a polynomial cut-off in the presence of noise in velocity. We rigorously prove the propagation of chaos for this interacting stochastic particle system. Taking the cut-off like N-δ with δ < 1/d in the force, we provide a quantitative error estimate between the empirical measure associated to that N-particle system and the solutions of the d-dimensional Vlasov-Poisson-Fokker-Planck (VPFP) system. We also study the propagation of chaos for the Vlasov-Fokker-Planck equation with less singular interaction forces than the Newtonian one.
| Original language | English |
|---|---|
| Article number | 1850039 |
| Journal | Communications in Contemporary Mathematics |
| Volume | 21 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 2019 Jun 1 |
Bibliographical note
Funding Information:JAC was partially supported by the EPSRC grant number EP/P031587/1. YPC was supported by NRF grant (Nos. 2017R1C1B2012918 and 2017R1A4A1014735) and POSCO Science Fellowship of POSCO TJ Park Foundation. SS was supported by the Fondation des Sciences Mathématiques de Paris and Université Paris- Sciences-et-Lettres. The authors would like to thank Maxime Hauray for many fruitful discussions.
Funding Information:
JAC was partially supported by the EPSRC grant number EP/P031587/1. YPC was supported by NRF grant (Nos. 2017R1C1B2012918 and 2017R1A4A1014735) and POSCO Science Fellowship of POSCO TJ Park Foundation. SS was supported by the Fondation des Sciences Mathématiques de Paris and Université Paris-Sciences-et-Lettres. The authors would like to thank Maxime Hauray for many fruitful discussions.
Publisher Copyright:
© 2019 The Author(s).
All Science Journal Classification (ASJC) codes
- Mathematics(all)
- Applied Mathematics