关于三维Navier-Stokes方程适定弱解奇异集的注记
偏微分方程分析
2017-11-01 v2
摘要
在本文中，设 表示三维Navier-Stokes方程适定弱解的可能内部奇异集。我们将该集合的已知上盒计数维数从[24]中的 改进到 。此外，还证明了 ，这扩展了Choe和Lewis [3, J. Funct. Anal., 175: 348-369, 2000]以及Choe和Yang等人 [4, Comm. Math. Phys, 336: 171-198, 2015]此前关于通过对数因子改进经典Caffarelli-Kohn-Nirenberg定理的相关结果。该证明受Guevara和Phuc在[7, Calc. Var. 56:68, 2017]中证明的新 -正则性准则的启发。
引用
@article{arxiv.1709.01319,
title = {Remarks on the singular set of suitable weak solutions to the 3D Navier-Stokes equations},
author = {Wei Ren and Yanqing Wang and Gang Wu},
journal= {arXiv preprint arXiv:1709.01319},
year = {2017}
}
备注
In this version, Theorem 1.3 and its proof are revised. The reason for the modification of Theorem 1.3 is to answer a issue proposed by the reviewer. An author is added