平面不可压缩的Navier-Stokes方程的一个新七模截断

数学季刊 ›› 2012, Vol. 27 ›› Issue (1): 11-17.

平面不可压缩的Navier-Stokes方程的一个新七模截断

1. College of Science, Liaoning University of Technology 2. College of Information Science and Engineering, Northeastern University

收稿日期:2007-05-25 出版日期:2012-03-30 发布日期:2023-03-31
作者简介:WANG He-yuan(1963-), male, native of Jinzhou, Liaoning, a professor of Liaoning University of Technology, engages in bifurcation theory and numerical analysis.
基金资助:
Supported by the Natural Science Foundation of China(41174090)

A New Seven-modes Truncation of the Plane Incompressible Navier-Stokes Equations

1. College of Science, Liaoning University of Technology 2. College of Information Science and Engineering, Northeastern University

Received:2007-05-25 Online:2012-03-30 Published:2023-03-31
About author:WANG He-yuan(1963-), male, native of Jinzhou, Liaoning, a professor of Liaoning University of Technology, engages in bifurcation theory and numerical analysis.
Supported by:
Supported by the Natural Science Foundation of China(41174090)

摘要/Abstract

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.

关键词: Navier-Stokes equations, the strange attractor, Lyapunov function, bifurcation; chaos

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.

Key words: Navier-Stokes equations, the strange attractor, Lyapunov function, bifurcation; chaos

中图分类号:

O175.14

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[J]. 数学季刊, 2012, 27(1): 11-17.

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, 27(1): 11-17.

[1]	郑治波, 张利萍, 郝晓红, 刘国旗, 孙江洁. 带有非线性项不可压Navier-Stokes方程整体性吸引子的存在性 [J]. 数学季刊, 2020, 35(1): 93-110.
[2]	秦玉明, 刘子丽. 第三型热弹Timoshenko型方程组指数衰减 [J]. 数学季刊, 2019, 34(2): 111-125.
[3]	漆勇方, 彭友花. 1到2分数阶非线性动力系统的稳定性分析[J]. 数学季刊, 2019, 34(2): 188-195.
[4]	王志军, 郝晓斌, 石东洋. 定常Navier-Stokes方程的一个二阶非协调三角型混合元格式[J]. 数学季刊, 2017, 32(1): 88-98.
[5]	张建林, 曹洁, 苏兴. 一维 Navier-Stokes-Korteweg 方程整体解的存在性唯一性和指数稳定性[J]. 数学季刊, 2016, 31(1): 27-38.
[6]	孙林林, 梁铁旺, 张建朋. 带有非齐次温度边界的一维可压缩粘性微极流体模型的局部正则性[J]. 数学季刊, 2014, 29(1): 129-141.
[7]	宋强. 具有CTL免疫反应的HTLV-I感染模型的全局稳定性[J]. 数学季刊, 2013, 28(4): 618-624.
[8]	张应奇, 慕小武, 刘彩侠. 一类带有外部扰动的模糊离散非线性系统的有限时间控制问题[J]. 数学季刊, 2011, 26(3): 426-433.
[9]	赵才地, 李用声, 周盛凡. 二维全平面上具线性阻尼Navier-Stokes方程组的整体吸引子和渐近光滑效应[J]. 数学季刊, 2009, 24(3): 445-452.
[10]	向红军, 王金华 . 具时滞的Hopfield网络周期解的指数稳定性[J]. 数学季刊, 2008, 23(2): 292-300.
[11]	陈金环, 高永良. 非光滑控制Lyapunov函数及非线性切换系统的镇定问题[J]. 数学季刊, 2007, 22(4): 586-591.
[12]	李宏飞, 罗学波. 多时滞非线性中立型反馈系统的鲁棒稳定性[J]. 数学季刊, 2006, 21(3): 416-422.
[13]	郭晓丽, 李蔚, 慕小武. 奇异离散线性系统的开关切换控制[J]. 数学季刊, 2006, 21(2): 283-287.