On the mean-field limit for the Vlasov-Poisson-Fokker-Planck system

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Huang, H

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Liu, JG

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Pickl, P

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2018-06-04T15:46:14Z

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2018-06-04T15:46:14Z

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2018-06-04T15:46:13Z

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We devise and study a random particle blob method for approximating the Vlasov-Poisson-Fokkker-Planck (VPFP) equations by a $N$-particle system subject to the Brownian motion in $\mathbb{R}^3$ space. More precisely, we show that maximal distance between the exact microscopic and the mean-field trajectories is bounded by $N^{-\frac{1}{3}+\varepsilon}$ ($\frac{1}{63}\leq\varepsilon<\frac{1}{36}$) for a system with blob size $N^{-\delta}$ ($\frac{1}{3}\leq\delta<\frac{19}{54}-\frac{2\varepsilon}{3}$) up to a probability $1-N^{-\alpha}$ for any $\alpha>0$, which improves the cut-off in [10]. Our result thus leads to a derivation of VPFP equations from the microscopic $N$-particle system. In particular we prove the convergence rate between the empirical measure associated to the particle system and the solution of the VPFP equations. The technical novelty of this paper is that our estimates crucially rely on the randomness coming from the initial data and from the Brownian motion.

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https://hdl.handle.net/10161/17119

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Springer Science and Business Media LLC

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math.AP

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math.AP

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math-ph

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math.DS

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math.MP

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On the mean-field limit for the Vlasov-Poisson-Fokker-Planck system

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Journal article

duke.contributor.orcid

Liu, JG|0000-0002-9911-4045

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Duke Kunshan University

pubs.organisational-group

Duke

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Duke Kunshan University Faculty

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