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arXiv · 1802.01929

Propagation of chaos for the VPFP 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 $N^{-\delta}$ with $\delta < 1/d$ 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 system. We also study the propagation of chaos for the Vlasov-Fokker-Planck equation with less singular interaction forces than the Newtonian one.

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José A. Carrillo, Young-Pil Choi, Samir Salem. 2018-02-06. Propagation of chaos for the VPFP equation with a polynomial cut-off. https://doi.org/10.1142/s0219199718500396

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