Abstract
We consider the well-posedness of the Keller–Segel system in uniformly local Lebesgue spaces. It is well known that the parabolic-elliptic Keller–Segel system is one of diffusion equations involving a nonlocal term. In this paper, we study the parabolic-elliptic Keller–Segel system by using only local properties of the initial data. Moreover, the unconditional uniqueness of mild solutions to the Keller–Segel system is studied using uniformly local Lebesgue spaces. We also consider the uniformly local almost periodicity of mild solutions.
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Acknowledgements
The author would like to thank the referee for kind suggestions and comments. The author wishes to express gratitude to Assistant Professor Ryuichi Sato for helpful discussions with him. The work of the author is supported by JSPS Grant-in-Aid for JSPS Fellows #19J20763.
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Suguro, T. Well-posedness and unconditional uniqueness of mild solutions to the Keller–Segel system in uniformly local spaces. J. Evol. Equ. 21, 4599–4618 (2021). https://doi.org/10.1007/s00028-021-00727-w
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DOI: https://doi.org/10.1007/s00028-021-00727-w