Abstract
We construct local strong solutions of Keller–Segel system of parabolic–elliptic type for arbitrary initial data in the homogeneous Besov space which is scaling invariant. We also show that the solution exists globally in time for small initial data. The solutions belong to the Lorentz space in time direction since our method relies on the maximal Lorentz regularity of heat equations.
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Takeuchi, T. Maximal Lorentz regularity for the Keller–Segel system of parabolic–elliptic type. J. Evol. Equ. 21, 4619–4640 (2021). https://doi.org/10.1007/s00028-021-00728-9
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DOI: https://doi.org/10.1007/s00028-021-00728-9