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,利用模式截断方法得到了一个全新的九模类Lorenz方程组,求出该方程组的平衡点,分析其稳定性等动力学行为,证明了该类Lorenz方程组混沌吸引子的存在性,对其进行全局稳定性分析,并对其动力学行为进行数值模拟.
This paper deals with a research on the Navier-Stokes equations for two-dimen -sional incompressible fluid on a torus. The new nine-mode Lorenz equations have been obtained by mode truncation. The equilibrium point has been figured out and the stability has been analyzed. The existence of the attractor has been proved, the global stability of the equations has bcen disscused and the dynamical behavior has been simulated numerically by computer.
出处
《应用数学学报》
CSCD
北大核心
2014年第3期507-515,共9页
Acta Mathematicae Applicatae Sinica
基金
辽宁省教育厅科研基金(L2013248)
锦州市科技专项基金(13A1D32)资助项目