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.

中文翻译：

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均匀局部空间中 Keller-Segel 系统温和解的适定性和无条件唯一性

我们考虑 Keller-Segel 系统在均匀局部 Lebesgue 空间中的适定性。众所周知，抛物线-椭圆 Keller-Segel 系统是涉及非局部项的扩散方程之一。在本文中，我们仅使用初始数据的局部特性来研究抛物线-椭圆 Keller-Segel 系统。此外，使用均匀局部 Lebesgue 空间研究了 Keller-Segel 系统的温和解的无条件唯一性。我们还考虑了温和解的均匀局部几乎周期性。