Propagation of chaos for a sub-critical Keller-Segel model

TL;DR

This paper proves the propagation of chaos for a sub-critical Keller-Segel model, demonstrating that the empirical measure of a stochastic particle system converges to the unique solution of the limiting PDE as particle number increases.

Contribution

It establishes well-posedness and propagation of chaos for the sub-critical Keller-Segel equation starting from the associated stochastic particle system.

Findings

Empirical measure converges to the unique solution of the limit equation.

Well-posedness of the sub-critical Keller-Segel equation is proven.

Propagation of chaos holds for the particle system.

Abstract

This paper deals with a sub-critical Keller-Segel equation. Starting from the stochastic particle system associated with it, we show well-posedness results and the propagation of chaos property. More precisely, we show that the empirical measure of the system tends towards the unique solution of the limit equation as the number of particles goes to infinity.