Propagation of chaos for the Vlasov-Poisson-Fokker-Planck equation with a polynomial cut-off

José A. Carrillo, Young Pil Choi, Samir Salem

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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 languageEnglish
Article number1850039
JournalCommunications in Contemporary Mathematics
Volume21
Issue number4
DOIs
Publication statusPublished - 2019 Jun 1

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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