The 2-D stochastic Keller-Segel particle model : existence and uniqueness

TL;DR

This paper introduces a stochastic particle system modeling the 2-D Keller-Segel equation and proves existence and uniqueness results for the system under subcritical mass conditions.

Contribution

It provides a rigorous stochastic framework for the Keller-Segel model, extending prior results by establishing existence and uniqueness for the particle system.

Findings

Existence of solutions for the stochastic model.

Uniqueness of solutions under certain conditions.

Applicable to all regimes below the critical mass.

Abstract

We introduce a stochastic system of interacting particles which is expected to furnish as the number of particles goes to infinity a stochastic approach of the 2-D Keller-Segel model. In this note, we prove existence and some uniqueness for the stochastic model for the parabolic-elliptic Keller-Segel equation, for all regimes under the critical mass. Prior results for existence and weak uniqueness have been very recently obtained by N. Fournier and B. Jourdain [6].