The local regularity conditions for the Navier–Stokes equations via one directional derivative of the velocity

被引：0
作者：
Zhengguang Guo
Petr Kucera
Zdenek Skalak
机构：
[1] Huaiyin Normal University,School of mathematics and statistics
[2] Czech Technical University,undefined
[3] Prague,undefined
来源：
Lithuanian Mathematical Journal | 2022年 / 62卷
关键词：
Navier–Stokes equations; suitable solution; conditional regularity; regularity criteria; 35Q30; 76D05;
D O I：
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中图分类号：
学科分类号：
摘要：
We study the local regularity of solutions to the Navier–Stokes equations. We show for a suitable weak solution (u, p) on an open space-time domain D that if ∂3u∈LtpLxqD\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\partial}_3u\in {L}_t^p{L}_x^q(D) $$\end{document}, where 2/p + 3/q = 2 and q ∈ (27/16, 5/2), then the solution is regular in D.
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页码：333 / 348
页数：15
相关论文
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