| 平面不可压缩的Navier-Stokes方程的一个新七模截断(英文) |
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| 引用本文： | 王贺元,崔妍,黄敏.平面不可压缩的Navier-Stokes方程的一个新七模截断(英文)[J].数学季刊,2012(1):11-17. |
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| 作者姓名： | 王贺元 崔妍 黄敏 |
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| 作者单位： | College of Science,Liaoning University of Technology;College of Information Science and Engineering,Northeastern University |
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| 基金项目： | Supported by the Natural Science Foundation of China(41174090) |
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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.
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| 关 键 词： | Navier-Stokes equations the strange attractor Lyapunov function bifurcation chaos |
A New Seven-modes Truncation of the Plane Incompressible Navier-Stokes Equations |
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| WANG He-yuan,CUI Yan,HUANG Min.A New Seven-modes Truncation of the Plane Incompressible Navier-Stokes Equations[J].Chinese Quarterly Journal of Mathematics,2012(1):11-17. |
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| Authors: | WANG He-yuan CUI Yan HUANG Min |
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| Institution: | 1.College of Science,Liaoning University of Technology,Jinzhou 121001,China;2.College of Information Science and Engineering,Northeastern University,Shenyang 110819,China) |
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| Abstract: | 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. |
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| Keywords: | Navier-Stokes equations the strange attractor Lyapunov function bifurcation chaos |
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