On the stability of critical chemotactic aggregation

TL;DR

This paper investigates the stability and formation of singularities in the 2D Patlak-Keller-Segel chemotaxis model, providing a detailed description of the aggregation process for radially symmetric data.

Contribution

It introduces a stable mechanism for singularity formation and offers a comprehensive analysis of the aggregation process in the model.

Findings

Existence of a stable singularity formation mechanism

Complete description of the aggregation process

Insights into stability for radially symmetric initial data

Abstract

We consider the two dimensional parabolic-elliptic Patlak-Keller-Segel model of chemotactic aggregation for radially symmetric initial data. We show the existence of a stable mechanism of singularity formation and obtain a complete description of the associated aggregation process.