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Maximal Lorentz regularity for the Keller–Segel system of parabolic–elliptic type
Journal of Evolution Equations ( IF 1.1 ) Pub Date : 2021-06-10 , DOI: 10.1007/s00028-021-00728-9
Taiki Takeuchi

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.



中文翻译:

抛物线-椭圆型 Keller-Segel 系统的最大洛伦兹正则性

我们在尺度不变的齐次 Besov 空间中为任意初始数据构造抛物线-椭圆型 Keller-Segel 系统的局部强解。我们还表明,对于小的初始数据,该解决方案在全球范围内及时存在。解在时间方向上属于洛伦兹空间,因为我们的方法依赖于热方程的最大洛伦兹正则性。

更新日期:2021-06-11
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