Global well-posedness for nonlocal fractional Keller–Segel systems in critical Besov spaces

In this paper, we study Keller–Segel systems with fractional diffusion and a nonlocal term. We establish the global existence, uniqueness and stability of solutions for systems with small initial data in critical Besov spaces. Our main tools are the Lp−LqLp−Lq estimates for e−t(−Δ)θ/2 in Besov spaces and the perturbation of linearization.