Besov型空间中Navier-Stokes初值问题的尖锐适定性与不适定性
偏微分方程分析
2018-04-03 v2
摘要
我们证明当第二指标不小于某临界值时，Navier-Stokes初值问题在对数精细Besov空间中是适定的；而当第二指标小于该临界值时，在此类空间中是不适定的。适定性结果通过使用由某些Hardy-Littlewood型不等式得到的一些尖锐双线性估计来证明。不适定性断言通过改进Wang [18]和Yoneda [20]的论证来证明。
引用
@article{arxiv.1505.00865,
title = {Sharp well-posedness and ill-posedness of the Navier-Stokes initial value problem in Besov-type spaces},
author = {Shangbin Cui},
journal= {arXiv preprint arXiv:1505.00865},
year = {2018}
}
备注
This is the second version of the paper with the same title publicized in ArXiv under the number 1505.00865. It remedies the incorrect proof of Lemma 4.2 of the previous version and some other small mistakes. The main result of this paper has been written in the book of Lemari\'e-Rieusset "The Navier-Stokes Problem in the 21st Century" (CRC press, 2016) as Theorem 9.6 (without proof)