Mean--field limit of a particle approximation of the one-dimensional parabolic--parabolic Keller-Segel model without smoothing

TL;DR

This paper proves the well-posedness of a singular particle system and demonstrates propagation of chaos towards the 1D Keller-Segel model, advancing understanding of particle approximations in chemotaxis modeling.

Contribution

It introduces a novel particle approximation for the Keller-Segel model and establishes rigorous propagation of chaos results without smoothing techniques.

Findings

Proved well-posedness of the singular particle system

Established propagation of chaos towards the Keller-Segel PDE

Provided a new framework for particle approximations in chemotaxis

Abstract

In this work, we prove the well--posedness of a singularly interacting stochastic particle system and we establish propagation of chaos result towards the one-dimensional parabolic-parabolic Keller-Segel model.