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A new approach to the
mean-field limit of Vlasov–Fokker–Planck equations
Didier Bresch, Pierre-Emmanuel Jabin and Juan Soler |
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Vol. 18 (2025), No. 4, 1037–1064
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Abstract |
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We introduce a novel approach to the mean-field limit of stochastic systems of interacting particles, leading to the first ever derivation of the mean-field limit to the Vlasov–Poisson–Fokker–Planck system for plasmas in dimension together with a partial result in dimension . The method is broadly compatible with second-order systems that lead to kinetic equations and it relies on novel estimates on the BBGKY hierarchy. By taking advantage of the diffusion in velocity, those estimates bound weighted norms of the marginals or observables of the system, uniformly in the number of particles. This allows us to qualitatively derive the mean-field limit for very singular interaction kernels between the particles, including repulsive Poisson interactions, together with quantitative estimates for a general kernel in . |
Keywords
kinetic equations, mean-field limit,
Vlasov–Poisson–Fokker–Planck, marginals
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Mathematical Subject Classification
Primary: 35Q70, 35Q83, 60H10, 70F45, 82D10
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Milestones
Received: 7 March 2023
Revised: 21 September 2023
Accepted: 21 December 2023
Published: 27 March 2025
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Authors |
| Didier Bresch | |
| Laboratoire de Mathématiques UMR5127
CNRS Université Savoie Mont Blanc Le Bourget du Lac France |
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| Pierre-Emmanuel Jabin | |
| Department of Mathematics Pennsylvania State University University Park, PA United States |
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| Juan Soler | |
| Departamento de Matemática
Aplicada Facultad de Ciencias Universidad de Granada Granada Spain |
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| © 2025 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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