Global existence of large solutions for the parabolic-elliptic Keller-Segel system in Besov type spaces

TL;DR

This paper proves the global existence of large solutions for the Keller-Segel system in Besov spaces, showing solutions can exist even with arbitrarily large initial data norms.

Contribution

It establishes the global existence of solutions in Besov spaces for large initial data, extending previous results to broader initial conditions.

Findings

Global smooth solutions exist for large initial data in Besov spaces.

The initial data can have arbitrarily large norms in the Besov space.

The results apply to the parabolic-elliptic Keller-Segel system.

Abstract

In this paper, we investigate global existence of large solutions for the parabolic-elliptic Keller-Segel system in the homogeneous Besov type spaces. A class of initial data was presented, generating a global smooth solution although the $\dot{B}^{-2}_{\infty,\infty}$-norm of the initial data may be chosen arbitrarily large.