Blowing up radial solutions in the minimal Keller-Segel model of chemotaxis

TL;DR

This paper investigates conditions under which radially symmetric solutions to a basic chemotaxis model blow up, using Morrey space norms to establish criteria for such singularities in multiple dimensions.

Contribution

It introduces new blowup criteria based on Morrey space norms for the minimal Keller-Segel chemotaxis model, advancing understanding of solution singularities.

Findings

Blowup criteria derived in terms of Morrey space norms.

Applicable to radially symmetric solutions in multiple dimensions.

Provides conditions predicting finite-time blowup.

Abstract

We consider the simplest parabolic-elliptic model of chemotaxis in the whole space in several dimensions. Criteria for the blowup of radially symmetric solutions in terms of suitable Morrey spaces norms are derived.