A Five-Dimensional System of Navier-Stokes Equation for a Two-Dimensional Incompressible Fluid on a Torus

被引：0

作者：

Wang Heyuan ^{[1
]}

Li Kaitai ^{[2
]}

机构：

[1] Liaoning Univ Technol, Coll Sci, Jinzhou 121001, Peoples R China

[2] Xi An Jiao Tong Univ, Coll Sci, Xian 710049, Peoples R China

来源：

JOURNAL OF PARTIAL DIFFERENTIAL EQUATIONS | 2016年 / 29卷 / 04期

关键词：

Navier-Stokes equation; strange attractor; Lyapunov function; bifurcation; chaos;

D O I：

10.4208/jpde.v29.n4.1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A five-mode truncation of Navier-Stokes equation for a two-dimensional incompressible fluid on a torus is studied. Its stationary solutions and stability are presented, the existence of attractor and the global stability of the system are discussed. The whole process, which shows a chaos behavior approached through an involved sequence of bifurcations with the changing of Reynolds number, is simulated numerically. Based on numerical simulation results of bifurcation diagram, Lyapunov exponent spectrum, Poincare section, power spectrum and return map of the system are revealed.

引用

页码：255 / 268

页数：14

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