Limites de champ moyen pour des noyaux singuliers et applications au modèle de Patlak–Keller–Segel

Translated title of the contribution: On mean-field limits and quantitative estimates with a large class of singular kernels: Application to the Patlak–Keller–Segel model

Didier Bresch, Pierre Emmanuel Jabin, Zhenfu Wang

Research output: Contribution to journalArticlepeer-review

Abstract

In this note, we propose a modulated free energy combination of the methods developed by P.-E. Jabin and Z. Wang [Inventiones (2018)] and by S. Serfaty [Proc. Int. Cong. Math. (2018) and references therein] to treat more general kernels in mean-field limit theory. This modulated free energy may be understood as introducing appropriate weights in the relative entropy developed by P.-E. Jabin and Z. Wang (in the spirit of what has been recently developed by D. Bresch and P.-E. Jabin [Ann. of Math. (2) (2018)]) to cancel the most singular terms involving the divergence of the flow. Our modulated free energy allows us to treat singular potentials that combine 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 the Patlak–Keller–Segel system in subcritical regimes, is obtained.

Translated title of the contributionOn mean-field limits and quantitative estimates with a large class of singular kernels: Application to the Patlak–Keller–Segel model
Original languageFrench
Pages (from-to)708-720
Number of pages13
JournalComptes Rendus Mathematique
Volume357
Issue number9
DOIs
StatePublished - Sep 2019

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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