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

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.