Title: Large global-in-time solutions to a nonlocal model of chemotaxis,
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.