Large stochastic systems of interacting particles | Vidéo | Carmin.tv

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Large stochastic systems of interacting particles

De Pierre-Emmanuel Jabin

many-particle systems

Apparaît dans la collection : Jean Morlet Chair 2021- Conference: Kinetic Equations: From Modeling Computation to Analysis / Chaire Jean-Morlet 2021 - Conférence : Equations cinétiques : Modélisation, Simulation et Analyse

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.

Informations sur la vidéo

Date de captation 23/03/2021
Date de publication 09/04/2021
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.19734403
Citer cette vidéo Jabin, Pierre-Emmanuel (23/03/2021). Large stochastic systems of interacting particles. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19734403
URL https://dx.doi.org/10.24350/CIRM.V.19734403

Domaine(s)

Bibliographie

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, et al. Mean field limit for Coulomb-type flows. Duke Mathematical Journal, 2020, vol. 169, no 15, p. 2887-2935. - http://dx.doi.org/10.1215/00127094-2020-0019

Codes MSC

Document(s)

https://www.cirm-math.fr/RepOrga/2355/Slides/slide_Pierre-Emmanuel_JABIN.pdf

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