Global Weak Solutions to One-Dimensional Compressible Navier-Stokes Equations with Density-Dependent Viscosity Coefficients

We prove the global existence of weak solutions of the one-dimensional compressible Navier-stokes equations with density-dependent viscosity. In particular, we assume that the initial density belongs to L^1 and L^∞, module constant states at x = -∞ and x = ＋∞, which may be different. The initial vacuum is permitted in this paper and the results may apply to the one-dimensional Saint-Venant model for shallow water.     

A remark on free boundary problem of 1‐D compressible Navier–Stokes equations with density‐dependent viscosity

In this paper, we prove the existence and uniqueness of the weak solution of the one‐dimensional compressible Navier–Stokes equations with density‐dependent viscosity µ(ρ)=ρ^θ with θ∈(0, γ?2], γ>1. The initial data are a perturbation of a corresponding steady solution and continuously contact with vacuum on the free boundary. The obtained results apply for the one‐dimensional Siant–Venant model of shallow water and generalize ones in (Arch. Rational Mech. Anal. 2006; 182: 223–253). Copyright © 2009 John Wiley & Sons, Ltd.     

微乳液法制备水溶性双亲丙烯酰胺-苯乙烯嵌段共聚物

分别以十二烷基硫酸钠 (SDS)、壬基酚聚氧乙烯醚 (OP 10 )为表面活性剂 ,丙烯酰胺 (AM)的水溶液为连续相 ,苯乙烯 (St)为分散相 ,构成微乳液共聚合体系 ,合成了水溶性双亲嵌段共聚物 ,并通过荧光探针技术、差示扫描量热 (DSC)测试及流变性能的测定表征了共聚物的嵌段性结构 ,用红外光谱 (FTIR)及紫外光谱 (UV)分析了共聚物的化学组成     

Remark on stability of rarefaction waves to the one‐dimensional compressible Navier–Stokes equations with density‐dependent viscosity coefficient

In this paper, we study one‐dimensional compressible isentropic Navier–Stokes equations with density‐dependent viscosity. We can obtain the asymptotic stability of rarefaction waves for the compressible isentropic Navier–Stokes equations when the power of viscosity coefficient , which enlarge the range of α in the article [Jiu Q, Wang Y, Xin ZP, Communication in Partial Differential Equations 2011; 36: 602‐634]. Copyright © 2013 John Wiley & Sons, Ltd.     

聚合物燃烧方法制备Co_3O_4纳米粒子

纳米粒子因其独特的物理化学特性成为近年来材料科学领域的研究热点 .制备方法是获得性能优越材料的关键 .Co3 O4 具有正常的尖晶石结构 ,Co2 占据八面体位置 ,在空气中低于 80 0℃时十分稳定 ,是优良的催化剂材料 [1,2 ] ,采用燃烧方法可通过控制反应条件在不发生沉淀的情况下获得化学组成均匀的复合氧化物粉体[4～ 7] .本文利用聚合物燃烧方法探索制备粒径均匀、分散性好的立方 Co3 O4 纳米粒子 .选择聚乙烯醇 ( PVA)的原因是其分子内包含大量的羟基极性基团 ,能与金属离子尤其是过渡金属离子形成良好的化学键 ,促使金属离子在 PVA…     

Graphdiyne Oxide Modified NiOx for Enhanced Charge Extraction in Inverted Planar MAPbl3 Perovskite Solar Cells

The interface defects and nickel vacancies of the NiOx lead to interface charge recombination,which limits its application in perovskite solar cells.Here,graphdiyne oxide(GDYO)was added to NiOx as an inorganic hole transporting material.It is found that the average carrier lifetime declined from 29.2 ns to 5.4 ns and the recombination resistance increased significantly after the GDYO adding determined by the time-resolved photoluminescence and electrochemical impedance spectroscopy analysis.We further demonstrated that the GDYO adding to NiOx effectively improved the charge extraction,accelerated the charge transportation and suppressed the charge recombination.Consequently,the optimized NiOx(GDYO)-based cell showed superior performance with a higher fill factor(81.99％)and improved stability with respect to the reference device.This method provides a new method for property regulation of NiOx in inverted planar MAPbl3 perovskite solar cells.     

Smooth Approximations and Exact Solutions of the 3D Steady Axisymmetric Euler Equations

In this paper, we prove that a class of C ¹-smooth approximate solutions {u ^ε, p ^ε} to the 3D steady axisymmetric Euler equations will converge strongly to 0 in . The main assumptions are that the approximate solutions have uniformly finite energy and approach a constant state at far fields. We also show a Liouville type theorem that there are no non-trivial C ¹-smooth exact solutions with finite energy and uniform constant state at far fields. The research is partially supported by National Natural Sciences Foundation of China (No. 10871133 & No. 10771177). The research is partially supported by Zheng Ge Ru Funds, Hong Kong RGC Emarked Research Grant CUHK4028/04P and CUHK4040/06P, RGC Central Allocation Grant CA 05/06. SC01, and a grant from Northwest University, Xi’an, PRC.     

Asymptotic Behaviors of the Solutions to Scalar Viscous Conservation Laws on Bounded Interval

Abstract This paper concerns the asymptotic behaviors of the solutions to the initial-boundary value prob-lem for scalar viscous conservations laws u_t+f(u)_x=u_(xx) on[0,1],with the boundary condition u(0,t) =u_,u(1,t)=u_+ and the initial data u(x,0)=u_0(x,0)=u_0(x),where u_≠u_+ and f is a given function satisfyingf'(u)>0 for u under consideration.By means of energy estimates method and under some more regular condi-tions on the initial data,both the global existence and the asymptotic behavior are obtained.When u_u_+, which corresponds to shock waves in inviscid conservation laws, it is established for weak shockwaves,which means that │u_-u_+│is small.Moreover,exponential decay rates are both given.     

Existence of weak solutions of 2-D Euler equations with initial vorticityω 0∈L(log+ L) α (α>0)

It is proved that there exist global weak solutions of 2-D Euler equations inR ² under the assumption that the initial vorticity belongs to a kind of wider spaces,L ¹L(log⁺ L) (>0), which are Orlicz spaces containing spacesL ^p L ¹,L(log⁺ L) L (>1/2) and so on. This result improves on that of [2], [4], [11]. Moreover, these solutions are obtained by vanishing the viscosity term of Navier-Stokes equations.