Quantitative approximation of nonlinear Fokker-Planck equations with singular potential by interacting particle systems - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2020

Quantitative approximation of nonlinear Fokker-Planck equations with singular potential by interacting particle systems

Résumé

We propose a new approach to show quantitative estimates for solutions of nonlinear Fokker-Planck equations with singular potential by stochastic interacting particle systems. Our result only requires very weak regularity on the interaction kernel, including the Biot-Savart kernel, the family of Keller-Segel kernels in arbitrary dimension, and more generally singular Riesz kernels. The proof is based on a semigroup approach, and we also exploit the regularity of the solutions of the limiting equation.
Fichier principal
Vignette du fichier
GeneralKernel_Hal.pdf (588.19 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02914779 , version 1 (12-08-2020)
hal-02914779 , version 2 (12-11-2020)
hal-02914779 , version 3 (29-12-2020)
hal-02914779 , version 4 (27-06-2022)

Identifiants

  • HAL Id : hal-02914779 , version 1

Citer

Christian Olivera, Alexandre Richard, Milica Tomasevic. Quantitative approximation of nonlinear Fokker-Planck equations with singular potential by interacting particle systems. 2020. ⟨hal-02914779v1⟩
460 Consultations
509 Téléchargements

Partager

Gmail Facebook X LinkedIn More