Various regularity estimates for the Keller-Segel-Navier-Stokes system in Besov spaces
Various regularity estimates for the Keller-Segel-Navier-Stokes system in Besov spaces
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DOI：
10.1016/j.jde.2022.10.035
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发表时间：
2023-01
影响因子：
2.4
通讯作者：
Taiki Takeuchi
中科院分区：
文献类型：
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作者：
Taiki Takeuchi
我们证明了Keller-Segel-Navier-Stokes系统的局部适定性，其初始数据在标度不变的Besov空间中，如果初始数据足够小，则解在时间上全局存在。我们还揭示了该解在时间方向上属于Lorentz空间，而在空间和时间上是光滑的。在一定的条件下，得到了解的极大正则性估计。我们进一步证明了，如果初始数据具有更高的k，则解具有额外的k。这个结果意味着整体解在初始数据空间的同一范数下随着极限t→∞而衰减。我们关于洛伦兹正则性估计的结果是基于Kozono-Shimizu（2019）[26]的策略。
We show the local well-posedness for the Keller-Segel-Navier-Stokes system with initial data in the scaling invariant Besov spaces, where the solution exists globally in time if the initial data is sufficiently small. We also reveal that the solution belongs to the Lorentz spaces in time direction, while the solution is smooth in space and time. Moreover, we obtain the maximal regularity estimates of solutions under the certain conditions. We further show that the solution has the additional regularities if the initial data has higher regularities. This result implies that global solutions decay as the limit t→∞ in the same norm of the space of the initial data. Our results on the Lorentz regularity estimates are based on the strategy by Kozono-Shimizu (2019)[26].