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.
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Ke et al. (2026) studied this question.
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