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THE C^k INSTABILITY OF navier-stokes equation APPEND-ING POLYNOMIALS OF UNKNOWN FUNCTIONS

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Applied Mathematics and Mechanics(English Edition) 2000年第12期21卷 1440-1449页

作者：何幼桦施惟慧 Department of Mathematics Shanghai University Shanghai P R China

Applying the theory of stratification, the solution space structure about a class of deformed navier-stokes equation is determined. It is proved that such kind of equation has no C-k( k greater than or equal to2) stab... 详细信息

关键词： navier-stokes equation unstable equation strate transversale

RESIDUAL A POSTERIORI ERROR ESTIMATE TWO-GRID METHODS FOR THE STEADY (navier-stokes) equation WITH STREAM FUNCTION FORM

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Applied Mathematics and Mechanics(English Edition) 2004年第5期25卷 546-559页

作者：任春风马逸尘 College of Science Xi'an Jiaotong University

Residual based on a posteriori error estimates for conforming finite element solutions of incompressible navier-stokes equations with stream function form which were computed with seven recently proposed two-level method were derived. The posteriori error estimates contained additional terms in comparison to the error estimates for the solution obtained by the standard finite element method. The importance of these additional terms in the error estimates was investigated by studying their asymptotic behavior. For optimal scaled meshes, these bounds are not of higher order than of convergence of discrete solution.

关键词： two-level method navier-stokes equation residual a posteriori error estimate finite element method stream function form

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Communications in Theoretical Physics 2011年第10期56卷 745-750页

作者： I.F.Barna KFKI Atomic Energy Research Institute of the Hungarian Academy of Sciences Thermohydraulics Department(KFKI-AEKI)H-1525 BudapestP.O.Box 49Hungary

In this article we will present pure three dimensional analytic solutions for the navier-stokes and the continuity equations in Cartesian coordinates. The key idea is the three-dimensional generalization of the well-known self-similar Ansatz of Barenblatt. A geometrical interpretation of the Ansatz is given also. The results are the Kummer functions or strongly related. Our final formula is compared with other results obtained from group theoretical approaches.

关键词： navier-stokes equation self-similar solution

Impact of singularity of navier-stokes equation upon atmospheric motion equations

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Applied Mathematics and Mechanics(English Edition) 2007年第5期28卷 689-693页

作者：施惟慧王曰朋 Department of Mathematics Shanghai University Department of Mathematics Nanjing University of Information Science & Technology

Some conclusions about the smooth function classes stability for the basic system of equations of atmospheric motion and instability for navier-stokes equation are summarized. On the basis of this, by taking the basic system of equations of atmospheric motion via Boussinesq approximation as example to explain in detail that the instability about some simplified models of the basic system of equations for atmospheric motion is caused by the instability of navier-stokes equation, thereby, a principle to guarantee the stability of simplified equation is drawn in simplifying the basic system of equations.

关键词： equations of atmospheric approximation stability singular equation motion navier-stokes equation Boussinesq

ON THE FORMAL SOLUTION OF INITIAL VALUE PROBLEM OF navier-stokes equation

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Applied Mathematics and Mechanics(English Edition) 2000年第12期21卷 1432-1439页

作者：陈达段施惟慧 Department of Mathematics Shaghai University Shanghai P R China

A necessary and sufficient conditions of the existence of formal solution to the initial value problem of navier-stokes equation an R-3 x R are presented. A computation case is also given.

关键词： navier-stokes equation formal solution stratification equation secondaire

A Five-Dimensional System of navier-stokes equation for a Two-Dimensional Incompressible Fluid on a Torus

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Journal of Partial Differential equations 2016年第4期29卷 255-268页

作者： WANG Heyuan LI Kaitai College of Sciences Liaoning University of technology Jin'zhou 121001 China. College of Sciences Xi'an Jiaotong University Xi'an 710049 China

A five-mode truncation of navier-stokes equation for a two-dimensional incompressible fluid on a torus is studied. Its stationary solutions and stability are presented, the existence of attractor and the global stability of the system are discussed. The whole process, which shows a chaos behavior approached through an involved sequence of bifurcations with the changing of Reynolds number, is simulated numerically. Based on numerical simulation results of bifurcation diagram, Lyapunov exponent spectrum, Poincare section, power spectrum and return map of the system are revealed.

关键词： navier-stokes equation strange attractor Lyapunov function bifurcation chaos.

Solving navier-stokes equation by mixed interpolation method

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Journal of Southeast University(English Edition) 2006年第1期22卷 93-95页

作者：万水 Mogens Peter Nielsen 东南大学交通学院南京210096 丹麦技术大学土木工程系

The operator splitting method is used to deal with the navier-stokes equation, in which the physical process described by the equation is decomposed into two processes： a diffusion process and a convection process; and the finite element equation is established. The velocity field in the element is described by the shape function of the isoparametric element with nine nodes and the pressure field is described by the interpolation function of the four nodes at the vertex of the isoparametric element with nine nodes. The subroutine of the element and the integrated finite element code are generated by the Finite Element Program Generator （FEPG） successfully. The numerical simulation about the incompressible viscous liquid flowing over a cylinder is carded out. The solution agrees with the experimental results very well.

关键词： navier-stokes equation finite element method incompressible viscous flow mixed interpolation method

APPROXIMATE SOLUTION OF navier-stokes equation FOR VISCOUS FLOW OF FLOATING-RING BEARING

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APPROXIMATE SOLUTION OF NAVIER-STOKES EQUATION FOR VISCOUS F...

FULL DISCRETE TWO-LEVEL CORRECTION SCHEME FOR navier-stokes equationS

The Third International Conference on Dynamics, Vibration and Control

作者： Z Wang X.M.Ren and Z.H.Kang Institute of Vibration Engineering Northwestern Polytechnical University Xi’an 710072 China

＜正＞The floating-ring divides the oil film of the bearing into two layers:namely,the inner and the outer. As well-known,the tluid flow in the thin layer between two non-concentric rotating cylinders can be regarded as the flow between two concentric cylinders with a *** present investigation revels that the flow in the inner and outer layers can be also regarded as the flow between concentric rotating floating-rings with a ***,a new method is proposed for design of floating-ring in the high-speed rotating machinery.

关键词： navier-stokes equation floating-ring bearing basic flow tensor analysis bearing lubrication

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Journal of Computational Mathematics 2008年第2期26卷 209-226页

作者： Yanren Hou Liquan Mei College of Science Xi'an Jiaotong University Xi'an 710049 China

In this paper, a full discrete two-level scheme for the unsteady navier-stokes equations based on a time dependent projection approach is proposed. In the sense of the new projection and its related space splitting, non-linearity is treated only on the coarse level subspace at each time step by solving exactly the standard Galerkin equation while a linear equation has to be solved on the fine level subspace to get the final approximation at this time step. Thus, it is a two-level based correction scheme for the standard Galerkin approximation. Stability and error estimate for this scheme are investigated in the paper.

关键词： Two-level method Galerkin approximation Correction navier-stokes equation