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

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, Patr…

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 Navier-Stokes equations based on end-point Prodi-Serrin conditions, Applied Mathematics Letters, 83 (2018), 182—187], we take full advantage of the regula…

Regularity criteria for NSE 4: $\p_3u$

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…

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

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

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 equations: a remark on the role of the helicity. C. R. Math. Acad. Sci. Paris 347 (2009), no. 11-12, 613--618] 中, 作者证明了如果$$|u(x+y,t)\cdot \om(x,t)|\leq…

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 equations. Nonlinear Anal. 151 (2017), 265--273] 中, 作者证明了如果$$u\times \f{\om}{|\om|}\cdot \f{\vLm^\be u}{|\vLm^\be u|}\in L^p(0,T;L^q(\bbR^3)),\quad \f{2}{p}…

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. Phys. 53 (2012), no. 7, 073103, 6 pp] 中, 作者证明了如果$$\f{u}{|u|}\times \f{\om}{|\om|}\cdot \f{\n\times \om}{|\n\times \om|}$$充分小, 则解光滑.…

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 equations. J. Math. Fluid Mech. 12 (2010), no. 2, 171--180] 中, 作者证明了如果$$u\times\f{\om}{|\om|}\in L^p(0,T;L^q(\bbR^3)),\quad\f{2}{p}+\f{3}{q}=1,\quad 3<q\…

Research Papers

NSE, $\bbu$ [Papers]NSE, $u$, Lorentz space [Sohr, JEE, 2001] [Papers]NSE, $u$, Lorentz space [Bjorland-Vasseur, JMFM, 2011] [Papers]NSE, $u$, Lorentz space [Bosia-Pata-Robinson, JMFM, 2014] NSE, $u_3$ [Papers]NSE, $u_3$, Lebesgue space [NNP, QM, 200…

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 Besov spaces. Comput. Math. Appl. 75 (2018), no. 3, 1060--1065] 中, 我们讨论了 $$\bee\label{EL:Simple} \seddm{ \p_t\bbu +(\bbu\cdot\n)\bbu -\lap\bbu+…

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 zhangzujin361@163.com. [1] Jian Pan, Zujin Zhang, Xiangying Zhou, Optimal dynamic mean-variance asset-liability management under the Heston model, Advan…

乘积型Sobolev不等式

(Multiplicative Sobolev inequality). Let $\mu,\lambda$ and $\gamma$ be three parameters that satisfy $$\bex 1\leq \mu,\lm<\infty,\quad \frac{2}{\lm}+\frac{1}{\mu}>1\quad\mbox{and}\quad 1+\frac{3}{\gamma}=\frac{2}{\lm}+\frac{1}{\mu}. \eex$$ Assume $\…

[Papers]NSE, $u_3$, Lebesgue space [Jia-Zhou, NARWA, 2014]

$$\bex u_3\in L^\infty(0,T;L^\frac{10}{3}(\bbR^3)). \eex$$…

[Papers]NSE, $u_3$, Lebesgue space [Zhou-Pokorny, Nonlinearity, 2009]

$$\bex u_3\in L^p(0,T;L^q(\bbR^3)),\quad \frac{2}{p}+\frac{3}{q}=\frac{3}{4}+\frac{1}{2q},\quad \frac{10}{3}<q\leq\infty. \eex$$…

[Papers]NSE, $u_3$, Lebesgue space [Cao-Titi, IUMJ, 2008]

$$\bex u_3\in L^p(0,T;L^q(\bbR^3)),\quad \frac{2}{p}+\frac{3}{q}=\frac{2}{3}+\frac{2}{3q},\quad \frac{7}{2}<q\leq \infty. \eex$$…

[Papers]NSE, $u_3$, Lebesgue space [Kukavica-Ziane, Nonlinearity, 2006]

$$\bex u_3\in L^p(0,T;L^q(\bbR^3)),\quad \frac{2}{p}+\frac{3}{q}=\frac{5}{8},\quad \frac{24}{5}<q\leq \infty. \eex$$…

[Papers]NSE, $u_3$, Lebesgue space [NNP, QM, 2002; Zhou, JMPA, 2005]

$$\bex u_3\in L^p(0,T;L^q(\bbR^3)),\quad \frac{2}{p}+\frac{3}{q}=\frac{1}{2},\quad 6< q\leq \infty. \eex$$…

Hibernate框架之Criteria查询和注解（重点☆☆☆☆☆，难点☆☆☆）

写好一篇博客,不是容易的事.原因是:你要给自己以后看的时候,还能看懂,最重要的是当别人看到你的博客文章的时候,也一样很清楚的明白你自己写的东西.其实这也是一种成就感!! 对于每一个知识点,要有必要的解释语言及真实的代码. 今天呢,我就详细的写着 Hibernate框架的一种检索方式:Criteria查询.下面我写的这些案例,可能对于大牛没有什么好看的,但是对于初学者来说,却是一笔财富. 首先我们要知道的检索方式: Hibernate框架提供了5种检索对象的方式 1.导航对象图检索方…

Hibernate中Criteria的完整用法

1,CriteriaHibernate 设计了 CriteriaSpecification 作为 Criteria 的父接口,下面提供了 Criteria和DetachedCriteria .2,DetachedCriteriaSpring 的框架提供了getHibernateTemplate().findByCriteria(detachedCriteria) 方法可以很方便地根据DetachedCriteria 来返回查询结果.DetachedCriteria 提供了 2 个静态方法 for…

ACCEPTANCE CRITERIA FOR USER STORIES

One of the teams I have recently coached quickly got a grasp of how to phrase user stories but found it hard to relate to the concept of acceptance criteria. I wrote this short FAQ as an attempt to make it easier for my team to work with acceptance c…

Hibernate中使用Criteria查询

忽略一些配置,测试代码如下: Session session= HibernateUtil.getSession(); Transaction tx= session.beginTransaction(); Criteria criteria =session.createCriteria(Dept.class) List<Dept>list=criteria.list(); for(Dept dept:list){ syso(dept.getDeptName()); } tx.commit(…

Hibernate框架中Criteria语句

在Hibernate中有一种查询语句是Criteria查询(QBC查询),今天呢我们就一个个的详细的跟大家一起探讨Criteria语句的相关知识点案例前的准备 //插入测试数据,构建数据库 public static void insertInfo(){ //获取Session Session session=HibernateUtil.currentSession(); //开启事务 Transaction tx = session.beginTransaction(); //构建班级 G…

tomcat 7 WARNING: A context path must either be an empty string or start with a '/' and do not end with a '/'. The path [/] does not meet these criteria and has been changed to []

tomcat 7 WARNING: A context path must either be an empty string or start with a '/' and do not end with a '/'. The path [/] does not meet these criteria and has been changed to [] 解决方法: 将server.xml中的<Context docBase="../deploy" path="/&q…

[NHibernate]条件查询Criteria Query

目录写在前面文档与系列文章条件查询一个例子总结写在前面上篇文章介绍了HQL查询,我个人觉得使用ORM框架就是为了让少些sql,提高开发效率,而再使用HQL就好像还是使用sql,就觉得有点又回到使用sql的年代.但是完全不用hql也不是绝对的,HQL更接近原生态的sql,对于一些比较复杂的查询,HQL的作用就体现出来了.作为使用面向对象语言的程序员,有时更愿意采用面向对象的方式去思考问题,去实现查询,这就是本篇文章要学习的条件查询(Criteria Query). 文档与系列文章 […

Theoretical comparison between the Gini Index and Information Gain criteria

Knowledge Discovery in Databases (KDD) is an active and important research area with the promise for a high payoff in many business and scientific applications. One of the main tasks in KDD is classification. A particular efficient method for classif…

NHibernate系列文章二十三：NHibernate查询之Criteria查询（附程序下载）

摘要上一篇文章介绍了NHibernate HQL,他的缺点是不能够在编译时发现问题.如果数据库表结构有改动引起了实体关系映射的类有改动,要同时修改这些HQL字符串.这篇文章介绍NHibernate面向对象的Criteria查询.他提供了很多API接口,可以实现“私人订制”式的面向对象查询. 作为对照,本篇文章将上篇文章的八个HQL查询全部用Criteria查询写一遍,读者可以自己感受下他们之间的区别. 本篇文章的代码可以到NHibernate查询下载 1.创建Criteria对象,查询所有Cu…

hibernate HQL和Criteria

package com.test; import java.util.Date; import java.util.List; import org.hibernate.Query; import org.hibernate.Session; import com.entity.User; import com.hibernate.HibernateUtil; public class QueryTest { public static void main(String[] args) { Us…