In [Zhang, Zujin. Serrin-type regularity criterion for the Navier-Stokes equations involving one velocity and one vorticity component. Czechoslovak Math. J. 68 (2018), no. 1, 219--225], we give an affirmative answer to an open problem in [Penel, Patrick; Pokorn\'y, Milan. Some new regularity criteria for the Navier-Stokes equations containing gradient of the velocity. Appl. Math. 49 (2004), no. 5, 483--493], that is, whether or not we could obtain a regularity criterion involving only $u_3$ and $\om_3=\p_1u_2-\p_2u_1$. Our result reveals that if $$\bee\label{this} \bea u_3\in L^p(0,T;L^q(\bbR^3));&\quad \omega_3\in L^r(0,T;L^s(\bbR^3)),\\ \frac{2}{p}+\frac{3}{q}=1,\ 3<q\leq\infty;&\quad \frac{2}{r}+\frac{3}{s}=2,\quad \frac{3}{2}< s\leq \infty, \eea \eee$$ then the solution is smooth on $(0,T)$.

Regularity criteria for NSE 5: $u_3,\om_3$的更多相关文章

  1. 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 ...

  2. Regularity criteria for NSE 4: $\p_3u$

    In [Zhang, Zujin. An improved regularity criterion for the Navier–Stokes equations in terms of one d ...

  3. [Papers]NSE, $\n u_3$, Lebesgue space, [Pokorny, EJDE, 2003; Zhou, MAA, 2002]

    $$\bex \n u_3\in L^p(0,T;L^q(\bbR^3)),\quad \frac{2}{p}+\frac{3}{q}=\frac{3}{2},\quad 2\leq q\leq \i ...

  4. 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 ...

  5. 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 ...

  6. 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 ...

  7. 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 ...

  8. Research Papers

    NSE, $\bbu$ [Papers]NSE, $u$, Lorentz space [Sohr, JEE, 2001] [Papers]NSE, $u$, Lorentz space [Bjorl ...

  9. 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 ...

随机推荐

  1. .NET MVC全局异常处理（二）

    目录 .NET MVC全局异常处理(二) MVC过滤器Filter .NET MVC全局异常处理(二) 对上节的内容进行了补充 MVC过滤器Filter MVC有四种过滤器:Authorization ...

  2. 如何解决代码中if…else 过多的问题

    前言 if...else 是所有高级编程语言都有的必备功能.但现实中的代码往往存在着过多的 if...else.虽然 if...else 是必须的,但滥用 if...else 会对代码的可读性.可维护 ...

  3. bsp makefile2

    1. grep "bsp_dir" -r ./  -s  --exclude-dir "*.git" 用这个加快目录定位-- 2.编译所有子目录 for dir ...

  4. HBase案例：HBase 在人工智能场景的使用

    近几年来,人工智能逐渐火热起来,特别是和大数据一起结合使用.人工智能的主要场景又包括图像能力.语音能力.自然语言处理能力和用户画像能力等等.这些场景我们都需要处理海量的数据,处理完的数据一般都需要存储 ...

  5. PHP奇淫技巧

    https://www.jb51.net/list/list_67_1.htm PHP技巧:https://www.jb51.net/list/list_67_13.htm mysql三范式 1NF: ...

  6. 001_python多进程实例

    一.工作中需要执行zk数据对比,需要按照机器进行并发,举例以下的例子 # coding:utf8 # !/usr/bin/python import time from multiprocessing ...

  7. firewall centos

    firewall-cmd --add-port=8056/tcp    --临时增加端口 firewall-cmd --permanent --zone=public --add-port=6069/ ...

  8. elementUi源码解析(1)--项目结构篇

    因为在忙其他事情好久没有更新iview的源码,也是因为后面的一些组件有点复杂在考虑用什么方式把复杂的功能逻辑简单的展示出来,还没想到方法,突然想到element的组件基本也差不多,内部功能的逻辑也差不 ...

  9. Golang 入门 : 字符串

    在 Golang 中,字符串是一种基本类型,这一点和 C 语言不同.C 语言没有原生的字符串类型,而是使用字符数组来表示字符串,并以字符指针来传递字符串.Golang 中的字符串是一个不可改变的 UT ...

  10. 玩转3D Swiper美女性感秀之思路分析总结

    前言 继一次的3D魔方之后,这次利用CSS3的transform.translate.rotate.preserve-3d等结合JS的requestAnimationFrame.class带你一起玩转 ...