# Particle approximation of the $2$-$d$ parabolic-elliptic Keller-Segel system in the subcritical regime

Abstract : The parabolic-elliptic Keller-Segel partial differential equation is a two-dimensional model for chemotaxis. In this work we introduce a stochastic system of moderately interacting particles which converges, globally in time, to the solution to the Keller-Segel model in $2$-d. The advantage of our approach is that we show the convergence in a strong sense for all the subcritical values of the total mass, $M < 8\pi$.
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.inria.fr/hal-02537226
Contributor : Milica Tomasevic Connect in order to contact the contributor
Submitted on : Wednesday, April 8, 2020 - 5:05:04 PM
Last modification on : Tuesday, July 20, 2021 - 3:06:24 AM

### Identifiers

• HAL Id : hal-02537226, version 1
• ARXIV : 2004.03177

### Citation

Christian Olivera, Alexandre Richard, Milica Tomasevic. Particle approximation of the $2$-$d$ parabolic-elliptic Keller-Segel system in the subcritical regime. 2020. ⟨hal-02537226⟩

Record views