| Navier-Stokes方程五模类Lorenz方程组的动力学行为及数值仿真 |
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| 引用本文： | 王贺元.Navier-Stokes方程五模类Lorenz方程组的动力学行为及数值仿真[J].应用数学与计算数学学报,2010,24(2):13-22. |
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| 作者姓名： | 王贺元 |
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| 作者单位： | 辽宁工业大学理学院,锦州121001 |
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| 摘 要： | 本文对平面正方形区域上不可压缩的Navier-Stokes方程,进行傅立叶展开后,截断得到五模类Lorenz方程组.给出了该方程组定常解及其稳定性的讨论,证明了该方程组吸引子的存在性,并对其全局稳定性进行了分析和讨论,数值模拟了雷诺数在一定范围内变化时,类Lorenz方程组的动力学行为.
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| 关 键 词： | Navier-Stokes方程 奇怪吸引子 李雅普诺夫函数 |
The Dynamical Behavior and the Numerical Simulation of a Five-Modes Lorenz Equations of the Navier-Stokes Equations |
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| Wang Heyuan.The Dynamical Behavior and the Numerical Simulation of a Five-Modes Lorenz Equations of the Navier-Stokes Equations[J].Communication on Applied Mathematics and Computation,2010,24(2):13-22. |
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| Authors: | Wang Heyuan |
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| Institution: | Wang Heyuan School of Sciences,Liaoning University of Technology,Jin＇zhou 121001,China |
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| Abstract: | We study the dynamical behavior of a five-modes Lorenz equations of the navier-stokes equations for a two-dimensional incompressible fluid on a torus.The plane incompressible Navier-Stokes equations is expanded in fourier series on a torus,then a five-modes Lorenz equations is obtained.The stationary solution and their stability properties are presented,the existence of the attractor is proved,and the global stability of the equations is disscused. The dynamical behavior is simulated numerically by computer according to the changing of Reynolds number. |
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| Keywords: | the Navier-Stokes equations strange attractor Liapunov function |
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