On pointwise decay rates of time‐periodic solutions to the Navier–Stokes equation

We study the existence of a time‐periodic solution with pointwise decay properties to the Navier–Stokes equation in the whole space. We show that if the time‐periodic external force is sufficiently small in an appropriate sense, then there exists a time‐periodic solution $\{u,p\}$ of the Navier–Stokes equation such that $|{?}^j{u(t,x)|=O(|x|}^{1?n?j})$ and $|{?}^j{p(t,x)|=O(|x|}^{?n?j})(j=0,1,\dots )$ uniformly in $t\in \mathbb{R}$ as $|x|\to \infty$. Our solution decays faster than the time‐periodic Stokes fundamental solution and the faster decay of its spatial derivatives of higher order is also described.     

基于2,5-二溴对苯二甲酸配体的锌/钴配合物合成、晶体结构及性质

将有机物2,5-二溴对苯二甲酸(H₂L₁)和2,2′-联吡啶(L₂)作为双配体,使用溶剂热法和七水合硫酸锌(ZnSO₄·7H₂O)、六水合硝酸钴(Co(NO₃)₂·6H₂O)分别反应,得到配合物[Zn(L₁)(L₂)(H₂O)]_n(1)和配合物[Co(L₁)(L₂)(H₂O)]_n(2)。采用单晶X射线衍射、元素分析、红外光谱、紫外光谱、荧光光谱、热重分析等测试方法对这两种物质进行分析研究。单晶测试结果表明配合物1是单斜晶系,以Zn²⁺配位连接L^2-₁与L₂形成一维链状结构,各条链在分子间氢键和π…π共轭作用下有规律地堆叠形成三维网络结构。配合物2是三斜晶系,Co1离子和Co1ⁱ离子由H₂L₁上的羧酸氧原子O4和O4ⁱ连接,形成双齿螯合的配位结构单元,以Co²⁺配位连接 L^2-₁和L₂形成二维网格结构,各层在O—H…O分子间氢键和范德瓦耳斯力作用下有规律的堆叠形成三维网络结构。配合物1和2均含有芳香杂环、羧基杂环和氮杂环,具有良好的荧光性质和热稳定性,最大发射波长分别为345 nm和333 nm。     

A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems

In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results.