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

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 ${\dot{B}}_{\mathrm{\infty },\mathrm{\infty }}^{-2}$-norm of the initial data may be chosen arbitrarily large.