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The mean-field limit to the Vlasov-Poisson-Fokker-Planck system

By Pierre-Emmanuel Jabin

Appears in collection : Probability/PDE Interactions: Interface Models and Particle Systems / Interactions EDP/Probabilités : interfaces et systèmes de particules

We propose a modulated free energy which combines of the method previously developed by the speaker together with the modulated energy introduced by S. Serfaty. This modulated free energy may be understood as introducing appropriate weights in the relative entropy to cancel the more singular terms involving the divergence of the flow. This modulated free energy allows to treat singular interactions of gradient-flow type and allows potentials with large smooth part, small attractive singular part and large repulsive singular part. As an example, a full rigorous derivation (with quantitative estimates) of some chemotaxis models, such as Patlak-Keller Segel system in the subcritical regimes, is obtained. This is joint work with D. Bresch and Z. Wang.

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Citation data

  • DOI 10.24350/CIRM.V.19910103
  • Cite this video Jabin Pierre-Emmanuel (4/25/22). The mean-field limit to the Vlasov-Poisson-Fokker-Planck system. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19910103
  • URL https://dx.doi.org/10.24350/CIRM.V.19910103



  • BRESCH, Didier, JABIN, Pierre-Emmanuel, et WANG, Zhenfu. On mean-field limits and quantitative estimates with a large class of singular kernels: application to the Patlak–Keller–Segel model. Comptes Rendus Mathematique, 2019, vol. 357, no 9, p. 708-720. - https://doi.org/10.1016/j.crma.2019.09.007
  • JABIN, Pierre-Emmanuel et WANG, Zhenfu. Quantitative estimates of propagation of chaos for stochastic systems with $W^{-1,\infty}$ kernels. Inventiones mathematicae, 2018, vol. 214, no 1, p. 523-591. - https://doi.org/10.1007/s00222-018-0808-y
  • SERFATY, Sylvia. Mean field limit for Coulomb-type flows. Duke Mathematical Journal, 2020, vol. 169, no 15, p. 2887-2935. - https://doi.org/10.1215/00127094-2020-0019

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