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• W2979078950 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. Dans cette note, on propose une énergie libre modulée combinant les méthodes développées par P.-E. Jabin et Z. Wang [Inventiones (2018)] et par S. Serfaty [voir l'article de revue Proc. Int. Cong. Math. (2018) et ses références] pour traiter des noyaux plus généraux en théorie de la limite champ moyen. Cette énergie libre modulée consiste en l'introduction d'une famille de poids appropriés dans l'entropie relative développée par P.-E. Jabin et Z. Wang (dans le même esprit que dans le travail récent de D. Bresch et P.-E. Jabin [Ann. of Math. (2) (2018)]) pour compenser les termes les plus singuliers qui font intervenir la divergence du champ de vitesse. Comme exemple, une preuve avec estimation quantitative de la limite champ moyen vers le modèle de Patlak–Keller–Segel en régime sous-critique est obtenue. Notre méthode permet également de couvrir des potentiels singuliers qui peuvent combiner une partie réguliere, une petite partie singulière attractive et une grande partie singulière répulsive." @default.
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• W2979078950 date "2019-09-01" @default.
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• W2979078950 title "On mean-field limits and quantitative estimates with a large class of singular kernels: Application to the Patlak–Keller–Segel model" @default.
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• W2979078950 doi "https://doi.org/10.1016/j.crma.2019.09.007" @default.
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