Propagation of chaos for the Keller-Segel equation over bounded domains

TL;DR

This paper rigorously proves the propagation of chaos for the Keller-Segel equation with no-flux boundary conditions in bounded convex domains, establishing foundational results for stochastic and PDE well-posedness.

Contribution

It provides the first rigorous justification of propagation of chaos for the Keller-Segel model in bounded domains with no-flux boundary conditions.

Findings

Well-posedness of the stochastic particle system

Existence of bounded weak solutions for Keller-Segel

Propagation of chaos established in bounded domains

Abstract

In this paper we rigorously justify the propagation of chaos for the parabolic-elliptic Keller-Segel equation over bounded convex domains. The boundary condition under consideration is the no-flux condition. As intermediate steps, we establish the well-posedness of the associated stochastic equation as well as the well-posedness of the Keller-Segel equation for bounded weak solutions.