# Large global-in-time solutions to a nonlocal model of chemotaxis

## TL;DR

This paper develops a mathematical framework for global solutions to a chemotaxis model with fractional diffusion, establishing conditions for existence and blowup based on initial data norms.

## Contribution

It introduces new criteria for global existence and blowup of solutions in a nonlocal chemotaxis model with fractional diffusion.

## Key findings

- Global solutions constructed under optimal initial data conditions.
- Blowup criteria derived using Morrey space norms.
- Analysis of radial solutions in the nonlocal chemotaxis model.

## Abstract

We consider the parabolic-elliptic model for the chemotaxis with fractional (anomalous) diffusion. Global-in-time solutions are constructed under (nearly) optimal assumptions on the size of radial initial data. Moreover, criteria for blowup of radial solutions in terms of suitable Morrey spaces norms are derived.