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A New Seven-modes Truncation of the Plane Incompressible Navier-Stokes EquationsA New Seven-modes Truncation of the Plane Incompressible Navier-Stokes Equations 被引量：3

A New Seven-modes Truncation of the Plane Incompressible Navier-Stokes EquationsA New Seven-modes Truncation of the Plane Incompressible Navier-Stokes Equations
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摘要 A new seven-modes truncation of Fourier series of Navier-Stokes equations for a two-dimensional incompressible fluid on a torus is obtained.And its stationary solutions,the existence of attractor and the global stability of the equations are firmly proved.At the same time,several issues such as some basic dynamical behaviors and routs to chaos are shown numerically by changing Reynolds number.The system exhibits a stochastic behavior approached through an involved sequence of bifurcations. A new seven-modes truncation of Fourier series of Navier-Stokes equations for a two-dimensional incompressible fluid on a torus is obtained.And its stationary solutions,the existence of attractor and the global stability of the equations are firmly proved.At the same time,several issues such as some basic dynamical behaviors and routs to chaos are shown numerically by changing Reynolds number.The system exhibits a stochastic behavior approached through an involved sequence of bifurcations.
作者 WANG He-yuan CUI Yan HUANG Min
机构地区 College of Science College of Information Science and Engineering
出处 《Chinese Quarterly Journal of Mathematics》 CSCD 2012年第1期11-17,共7页 数学季刊（英文版）
基金 Supported by the Natural Science Foundation of China（41174090）
关键词 Navier-Stokes equations the strange attractor Lyapunov function bifurcation chaos Navier-Stokes equations； the strange attractor； Lyapunov function； bifurcation； chaos
分类号 O175.14 [理学—基础数学] O241.81 [理学—计算数学]
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参考文献11

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同被引文献32

  • 1王贺元,鞠春贤.四模Lorenz系统的动力学行为及其数值模拟[J].高等学校计算数学学报,2010,32(2):99-105. 被引量：12
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  • 4Boldrighini C,Franceschini V. A five-dimensional truncation of the plane incompressible Navier-Stokes equations[J].Communications in Mathematical Physics,1979,64(2):159-170.
  • 5Franceschini V,Zanasi R. Three-dimensional Navier-Stokes equations truncated on a torus[J]. Nonlinearity,1992,4(3):189-209.
  • 6Damei Li,Jun-an Lu,Xiaoqun Wu,et al. Estimating the bounds for the Lorenz family of chaotic systems[J]. Chaos,Solutiona and Fractals,2005,23(2):529-534.
  • 7Lorenz E N Deterministic Non-perils Flows[J].J.Atoms.Sd. 1963,20(2) : 130-141.
  • 8Valter Franceschini,Claudio Tebaldi.A Seven-modes Trunea- tion of the Plane Incompressble Navier--Stoke Equatlons[J]. Journal of Statistical Physics, 1981,25(3) :397-417.
  • 9Carlo Boldrighin, Vaker Franeesehini. A Five-dimen'sinal Truncation of the Plane Incompressible Navier-Stokes Equa- tions[J].Communications in Mathematical Physics, 1979,64 (2) :159-170.
  • 10Franceschini V,Zanasi R.Three dimensional Navier Stokes E- quations Truncated on a Torus [ J ]. Nonlinearity, 1992,4 (3) 189-209.

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二级引证文献4

Chinese Quarterly Journal of Mathematics
2012年 第1期

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