In [Zhang, Zujin. An improved regularity criterion for the Navier–Stokes equations in terms of one directional derivative of the velocity field. Bull. Math. Sci. 8 (2018), no. 1, 33--47] we have improved the results in Kukavica and Ziane (J Math Phys 48:065203, 2007) and Cao (Discrete Contin Dyn Syst 26:1141–1151, 2010) simultaneously. The result reads: the condition
$$\bee\label{me}\p_3\bbu\in L^p(0,T;L^q(\bbR^3)),\quad \frac{2}{p}+\frac{3}{q}=2,\quad \frac{3\sqrt{37}}{4}-3\leq q\leq 3\eee$$
could ensure the regularity of the solution.

see https://link.springer.com/article/10.1007/s13373-016-0098-x.

Regularity criteria for NSE 4: $\p_3u$的更多相关文章

  1. Regularity criteria for NSE 5: $u_3,\om_3$

    In [Zhang, Zujin. Serrin-type regularity criterion for the Navier-Stokes equations involving one vel ...

  2. Regularity criteria for NSE 6: $u_3,\p_3u_1,\p_3u_2$

    In [Zujin Zhang, Jinlu Li, Zheng-an Yao, A remark on the global regularity criterion for the 3D Navi ...

  3. Geometric regularity criterion for NSE: the cross product of velocity and vorticity 4: $u\cdot \om$

    在 [Berselli, Luigi C.; Córdoba, Diego. On the regularity of the solutions to the 3D Navier-Stokes eq ...

  4. Geometric regularity criterion for NSE: the cross product of velocity and vorticity 3: $u\times \f{\om}{|\om|}\cdot \f{\vLm^\be u}{|\vLm^\be u|}$

    在 [Chae, Dongho; Lee, Jihoon. On the geometric regularity conditions for the 3D Navier-Stokes equati ...

  5. Geometric regularity criterion for NSE: the cross product of velocity and vorticity 2: $u\times \om\cdot \n\times \om$

    在 [Lee, Jihoon. Notes on the geometric regularity criterion of 3D Navier-Stokes system. J. Math. Phy ...

  6. Geometric regularity criterion for NSE: the cross product of velocity and vorticity 1: $u\times \om$

    在 [Chae, Dongho. On the regularity conditions of suitable weak solutions of the 3D Navier-Stokes equ ...

  7. 液晶流在齐次 Besov 空间中的正则性准则

    在 [Zhang, Zujin. Regularity criteria for the three dimensional Ericksen–Leslie system in homogeneous ...

  8. Collections of Zujin Zhang's Published works

    I am not good, but I shall do my best to be better. Any questions, please feel free to contact zhang ...

  9. 乘积型Sobolev不等式

    (Multiplicative Sobolev inequality). Let $\mu,\lambda$ and $\gamma$ be three parameters that satisfy ...

随机推荐

  1. 【Python 15】分形树绘制3.0（递归函数）

    1.案例描述 将递归函数与循环函数结合绘制2.0的图形 2.案例分析 3.上机实验 """ 作者:梁斌 功能:五角星的绘制 版本:3.0 日期:03/08/2017 新增 ...

  2. 【Python 04】Python开发环境概述

    1.Python概述 Python是一种计算机程序设计语言,一个python环境中需要有一个解释器和一个包集合. (1)Python解释器 使用python语言编写程序之前需要下载一个python解释 ...

  3. js 设备判断（移动端pc端 安卓ios 微信）

    苹果安卓判断 $(function () { var u = navigator.userAgent, app = navigator.appVersion; var isAndroid = u.in ...

  4. FeathersJS简单使用指南，一个前端也能玩得转的后端框架

    官方文档 :https://docs.feathersjs.com/api/services.html#createdata-params 第一步,创建接口和服务 app.use("user ...

  5. Sklearn中的回归和分类算法

    一.sklearn中自带的回归算法 1. 算法 来自:https://my.oschina.net/kilosnow/blog/1619605 另外,skilearn中自带保存模型的方法,可以把训练完 ...

  6. sqlServer：行列转换之多行转一行

    1.建表:学生表(姓名,学科,成绩) CREATE TABLE teststudent(    stuname varchar(50) NULL,    subjects varchar(50) NU ...

  7. Auto Layout: Programmatic Constraints - BNR

    继续Auto Layout - BNR篇. 打开BNRDetailViewController.m文件,重载viewDidLoad方法来创建UIImageView对象.当你想要给通过加载NIB文件创建 ...

  8. OCR技术浅析-无代码篇（1）

    图像识别中最贴近我们生活的可能就是 OCR 技术了. OCR 的定义:OCR (Optical Character Recognition,光学字符识别)是指电子设备(例如扫描仪或数码相机)检查纸上打 ...

  9. CodeForces Round #544 Div.3

    A. Middle of the Contest 代码: #include <bits/stdc++.h> using namespace std; int h1, m1, h2, m2; ...

  10. input按钮使用方法