在 [Wei, Dongyi. Regularity criterion to the axially symmetric Navier-Stokes equations. J. Math. Anal. Appl. 435 (2016), no. 1, 402--413] 中, 作者证明了如果 $$\bex \sup_{t\geq 0} |ru^\tt(t,r,z)|\leq |\ln r|^{-\f{3}{2}},\quad r\leq \del_0\in\sex{0,\f{1}{2}}, \…

在 [Lei, Zhen; Zhang, Qi. Criticality of the axially symmetric Navier-Stokes equations. Pacific J. Math. 289 (2017), no. 1, 169--187] 中, 作者证明了如果 $$\bex \sup_{t\geq 0} |ru^\tt(t,r,z)|\leq C_*|\ln r|^{-2},\quad r\leq \del_0\in\sex{0,\f{1}{2}},\quad C_*<…

对轴对称 NSE, 我们改进了 [Pan, Xinghong. A regularity condition of 3d axisymmetric Navier-Stokes equations. Acta Appl. Math. 150 (2017), 103--109] 的正则性准则: $ru^r\geq -1$, 证明了如果 $ru^r\geq M$, 其中 $M>-2$ 是一个常数, 那么解光滑. 见 https://www.sciencedirect.com/science/artic…

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+…

http://blogs.mathworks.com/loren/2007/03/01/creating-sparse-finite-element-matrices-in-matlab/ Loren on the Art of MATLAB March 1st, 2007 Creating Sparse Finite-Element Matrices in MATLAB I'm pleased to introduce Tim Davis as this week's guest blogge…

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…

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…

The biggest difference between LES and RANS is that, contrary to LES, RANS assumes that \(\overline{u'_i} = 0\) (see the Reynolds-averaged Navier–Stokes equations). In LES the filter is spatially based and acts to reduce the amplitude of the scales o…

1. 方程  考虑 $\bbR^3$ 中有界区域 $\Omega$ 上如下的稳态流动: $$\bee\label{eq} \left\{\ba{ll} \Div(\varrho\bbu)=0,\\ \Div(\varrho\bbu\otimes \bbu) -\mu\lap \bbu -(\lambda+\mu)\n\Div\bbu +\n \varrho^\gamma =\varrho\bbf+\bbg. \ea\right. \eee$$ 2. 假设  先作一些初步的假设: 2.1. $\d…

5. 6 弹性静力学方程组的定解问题 5. 6. 1 线性弹性静力学方程组 1.  线性弹性静力学方程组 $$\bee\label{5_6_1_le} -\sum_{j,k,l}a_{ijkl}\cfrac{\p ^2u_k}{\p x_j\p x_l}=\rho_0b_i,\quad i=1,2,3.  \eee$$ 2.  (Korn 不等式) 设 $\Omega\subset{\bf R}^3$ 为有界区域, 则 $$\bex \exists\ C_0>0,\st \int_\Omega…