Particles approximation for some 1D kinetic Fokker-Planck equations with singular forces

Samir Salem

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arXiv · 1803.04017

Particles approximation for some 1D kinetic Fokker-Planck equations with singular forces

Samir Salem

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Abstract

In this paper we consider a system of $N$ particles on the real line evolving according to Newton's law, interacting through a singular (repulsive) force deriving from the potential $\frac{|x|^{1-\alpha}}{1-\alpha}$ with $\alpha \in (0,1/8)$ and Brownian force. Thanks to the entropy dissipation along the Liouville equation associated to this particles system and a control of the mechanic energy, we establish a quantitative estimate which enables to conclude to a convergence/consistency the particles system toward the limiting Vlasov-Fokker-Planck equation with singular force.

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Samir Salem. 2018-03-11. Particles approximation for some 1D kinetic Fokker-Planck equations with singular forces. https://arxiv.org/abs/1803.04017

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