Nonlocal parabolic-elliptic Keller-Segel systems with nonlinear growth and signal production

We study the nonlocal parabolic-elliptic Keller-Segel system in the entire space, incorporating nonlinearities for both cell kinetics and chemical signal production. Our aim is to establish a global solvability result with small data and prove the Hölder regularity for the obtained mild solution. The proofs are based on Fourier analysis, resolvent theory and fixed-point arguments.