Well-posedness and unconditional uniqueness of mild solutions to the Keller-Segel system in uniformly local spaces (Q2064557)

The parabolic-elliptic Keller-Segel system is studied in the whole space \(\mathbb R^n\) in the scale of uniformly local Lebesgue spaces with exponents \(r\ge n/2\). Results on local well-posedness and global-in-time well-posedness for small initial data are shown. Estimates of Bessel potentials are the key point of the analysis. The case \(r=n/2\) extends recent work [\textit{S. Cygan} et al., J. Evol. Equ. 21, No. 4, 4873--4896 (2021; Zbl 1487.35056)].