Global large solutions to the parabolic-parabolic Keller-Segel system in Besov spaces

The global well-posedness of Keller-Segel system ensures that bacteria do not aggregate excessively and the system can evolve normally. In this paper, we study the global well-posedness conditions of the parabolic-parabolic Keller-Segel system in Besov space. Under the small initial data of the densities of bacteria n0 and the chemical attractant c0, we establish the global existence of solutions. Furthermore, we also prove the global well-posedness under a partial large initial data condition which admit the initial density of bacteria can be large.