Local regularity conditions on initial data for local energy solutions of the Navier-Stokes equations
Local regularity conditions on initial data for local energy solutions of the Navier-Stokes equations
复制标题
纳维-斯托克斯方程局部能量解的初始数据的局部正则条件
DOI：
10.1007/s42985-021-00127-2
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Tsai Tai-Peng
中科院分区：
文献类型：
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作者：
Kang Kyungkeun;Miura Hideyuki;Tsai Tai-Peng
根据初值条件，我们研究了N-S方程的局部能量解的正则集。证明了如果初值的加权范数是有限的，则在由该权决定的时空超曲面所限定的区域内，所有局部能量解都是正则的。这一结果改进和推广了Caffarelli等人的定理C和D。(通信。纯苹果。数学课。35(6)：771-831,1982)和我们最近的论文(Kang等人，Pure Appl.肛门。Arxiv：2006.13145)。
We study the regular sets of local energy solutions to the Navier–Stokes equations in terms of conditions on the initial data. It is shown that if a weightednorm of the initial data is finite, then all local energy solutions are regular in a region confined by space-time hypersurfaces determined by the weight. This result refines and generalizes Theorems C and D of Caffarelli et al. (Comm. Pure Appl. Math. 35(6):771–831, 1982) and our recent paper (Kang et al., Pure Appl. Anal. arXiv:2006.13145) as well.