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Boundary Layer Theory and the Zero-Viscosity Limit of the Navier-Stokes Equation

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Acta Mathematica Sinica,English Series 2000年第2期16卷 207-218页

作者： Weinan E department of mathematics and Program in Applied and Computational mathematics,Princeton University,USA department of mathematics and Program in Applied and Computational mathematics Princeton University Princeton USA

A central problem in the mathematical analysis of fluid dynamics is the asymptotic limit of the fluid flow as viscosity goes to *** is particularly important when boundaries are present since vorticitv is typically generated at the boundary as a result of boundary layer *** boundary laver theory,developed by Prandtl about a hundred years ago,has become a standard tool in addressing these *** at the mathematical level,there is still a lack of fundamental understanding of these questions and the validity of the boundary layer *** this article,we review recent progresses on the analysis of Prandtl’s equation and the related issue of the zero-viscosity limit for the solutions of the Navier-Stokes *** also discuss some directions where progress is expected in the near future.

关键词： Boundary layer Blow-up Zero-viscosity limit Prandtl’s equation

Sufficient and Necessary Conditions for Limit Laws on Lag Sums of I. I. D. R. V. S

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Acta Mathematica Sinica,English Series 1998年第1期14卷 113-124页

作者： Zhang Lixin department of mathematics, Hangzhou University, Hangzhou 310028, China department of mathematics Hangzhou University Hangzhou China

Let {X, Xn;n≥1} be a sequence of i.i.d.r.v.s with EX=0 and EX2=σ2（0n=sum from i=1 to n Xl We obtain some sufficient and necessary conditions for lim sup max max |SN-SN-j|/{2σ2k（log N/k+log logk）}1/2=1 a,s to hol... 详细信息

关键词： Strong approximation Wiener process Lag sums of i.i.d.r.v.s Chernoff function

NONOVERLAPPING DOMAIN DECOMPOSITION METHOD WITH MIXED ELEMENT FOR ELLIPTIC PROBLEMS

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Journal of Computational mathematics 1996年第4期14卷 291-300页

作者： H.X. Rui(mathematics department, Shandong University, Jinan) 山东大学数学系山东济南

In this paper we consider the nonoverlapping domain decomposition method based on mixed element approximation for elliptic problems in two dimentional space. We give a kind of discrete domain decomposition iterative algorithm using mixed finite element, the subdomain problems of which can be implemented parallelly. We also give the existence, uniqueness and convergence of the approximate solution.

关键词： Zhang NONOVERLAPPING DOMAIN DECOMPOSITION METHOD WITH MIXED ELEMENT FOR ELLIPTIC PROBLEMS EV

Some Results on the Multiplier Conjecture for the Case n=5n_1

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Acta Mathematica Sinica,English Series 1998年第4期14卷 535-540页

作者： Wan Zhaoze, department of mathematics, Peking University, Beijing 100871, China department of mathematics Peking University Beijing China

Using the method presented in [1], we obtain some new results which improve on the result of MacFarland’s theorem (see [2]) in this case.

关键词： Difference sets Multiplier CH-equations

L-R smash products for bimodule algebras

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Progress in Natural Science:Materials International 2006年第6期16卷 580-587页

作者： ZHANG Liangyun (department of mathematics, Nanjing Agricultural University, Nanjing 210095, China department of mathematics, Nanjing University, Nanjing 210008, China) department of mathematics Nanjing Agricultural University Nanjing 210095 China department of mathematics Nanjing U-niversity Nanjing 210008 China

In this paper, we prove that the L-R smash product A(?)H is exactly the twisted smash product A * H if H is a finite dimensional cocommutative Hopf algebra, and give a sufficient and necessary condition for L-R smash products to be bialgebras (Hopf algebras) . For any finite dimensional coquasitriangular Hopf algebra (H,σ), we prove that the L-R smash product H(?)H is semisimple Artinian if H is semisimple and H * is unimodular. In particular, the L-R smash product D(H)* (?)D(H)* semisimple Artinian if the Drin-fel'd double D(H) is semisimple.

关键词： bimodule algebras L-R smash products coquasitriangular Hopf algebras Long bialgebras.

L~∞ CONVERGENCE OF TRUNC ELEMENT FOR THE BIHARMONIC EQUATION

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Journal of Computational mathematics 1997年第1期15卷 14-22页

作者： M. Wang(department of mathematics, Beijing University, Beijing, China) 北京大学数学系北京

The paper considers the L∞ convergence for TRUNC finite elements solving the boundary value problems of the biharmonic equation. The nearly optimal L∞ estimates for the error of first order derivatives are *** TRUNC plate element is proposed and developed by Argyris et al.. The numerical experiences show that the element has very good .***,[1l2]. The mathematicalproof of convergence of the TRUNC element is given by Shi Zong-ci in paper [3]. Thispaper will consider the L~∞ convergence for the TRUNC plate element.

关键词：双谐波方程边值问题收敛性有限元法

Numerical Dynamics of Coupled System of J-JType

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Communications in Nonlinear Science and Numerical Simulation 1997年第3期2卷 3-5页

作者： Wen Xin QIN (department of mathematics, Suzhou University) department of mathematics Suzhou University USA

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ＮｕｍｅｒｉｃａｌＤｙｎａｍｉｃｓｏｆＣｏｕｐｌｅｄＳｙｓｔｅｍｏｆＪＪＴｙｐｅＷｅｎＸｉｎＱＩＮ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｕｚｈｏｕＵｎｉｖｅｒｓｉｔｙ）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒｗｅｃｏｎｓｉｄｅｒｔｈ...

关键词： Coupled System of J J Type Global Attractor Numerical Dynamics Approximation

CONVERGENCE OF VORTEX WITH BOUNDARY ELEMENT METHODS

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Journal of Computational mathematics 1997年第2期15卷 127-137页

作者： P.W. Zhang(department of mathematics, Peking University) 北京大学数学系北京

In this work, the vortex methods for Euler equations with initial boundary value problem is considered, Poisson equations are solved using boundary element methods which can be seen to require less operations to compute the velocity field from the vorticity by Chorin([6]). We prove that the rate of convergence of the boundary element schemes can be independent of the vortex blob parameters.

关键词： Math CONVERGENCE OF VORTEX WITH BOUNDARY ELEMENT METHODS Zhang

REFINED CONNECTIVITY PROPERTIES OF ABELIAN CAYLEY GRAPHS

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Chinese Annals of mathematics,Series B 1998年第4期19卷 409-414页

作者： LI QIAOLIANG (department of Applied mathematics, Shanghai Jiaotong University, Shanghai 200030, ChinaPresend in department of mathematics, Hunan Normal University, Changsha 410082, China.)LI QIAO (department of Applied mathematics, Shanghai Jiaotong Univ department of Applied mathematics Shanghai Jiaotong University Shanghai 200030 China department of mathematics Hunan Normal University Changsha 410082 China

Restricted edge connectivity of a graph G is defined to be the minimum size |U| of a set U of edges such that G-U is disconnected and G-U contains no trivial component K1. The high order edge connectivity Ni, i1, is the number of edge outsets of size i. TO determine all Ni, i 1, for a general graph is NP-hard. In this paper, the authors evaluated the restricted edge connectivity and the high order edge connectivity Ni, 1 i -1, for any connected Abelian Cayley graphs explicitly.

关键词： Abelian Cayley graph Restricted edge connectivity High order edge connectivity