| 五模类Lorenz方程组吸引子的存在性及计算机模拟 |
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| 引用本文： | 汪敬贤,王贺元.五模类Lorenz方程组吸引子的存在性及计算机模拟[J].哈尔滨工业大学学报,2008,40(4):670-672. |
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| 作者姓名： | 汪敬贤 王贺元 |
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| 作者单位： | 1. 渤海大学,公共计算机教研部,锦州,121001
2. 辽宁工业大学,数理系,锦州,121001 |
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| 摘 要： | 为讨论类Lorenz方程组的动力学行为及数值模拟问题,采用新的截断模式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新五模类Lorenz方程组.分析和讨论方程组的全局稳定性,结果证明:方程组吸引子的存在性,得出了方程组的混沌行为的数值模拟结果.
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| 关 键 词： | Navier-Stokes方程 奇怪吸引子 李雅普诺夫函数 |
Existence of the attractor and the numerical simulation of a five- modes Lorenz equation |
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| WANG Jing-xian,WANG He-yuan.Existence of the attractor and the numerical simulation of a five- modes Lorenz equation[J].Journal of Harbin Institute of Technology,2008,40(4):670-672. |
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| Authors: | WANG Jing-xian WANG He-yuan |
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| Affiliation: | 1.Public Computer-education Department,Bohai University,Jinzou 121001,China;2.Dept.of Mathematics and physics,Liaoning University of Technology,Jinzhou 121001,China) |
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| Abstract: | To discuss the dynamical behaviors and the numerical simulation of a Lorenz-like equation,we expanded the plane incompressible Navier-Stokes equations in fourier series on a torus,then the new five-modes Lorenz equations were obtained.The global stability of the equations was discussed,and the existence of the attractor was proved,the chaos behavior was simulated numerically by a computer. |
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| Keywords: | the Navier-Stokes equations strange attractor Liapunov function |
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