Local criteria for blowup in two-dimensional chemotaxis models

TL;DR

This paper establishes criteria for finite-time blowup in 2D chemotaxis models, analyzing the effects of diffusion types and consumption terms on solution behavior.

Contribution

It introduces Morrey space-based blowup criteria for 2D Keller--Segel models with classical and fractional diffusion, and examines how consumption influences global existence.

Findings

Blowup criteria are derived using Morrey space norms.

Consumption term affects the global existence of solutions.

Results apply to both classical and fractional diffusion models.

Abstract

We consider two-dimensional versions of the Keller--Segel model for the chemotaxis with either classical (Brownian) or fractional (anomalous) diffusion. Criteria for blowup of solutions in terms of suitable Morrey spaces norms are derived. Moreover, the impact of the consumption term on the global-in-time existence of solutions is analyzed for the classical Keller--Segel system.