摘要
本文研究二维全空间上线性阻尼Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程的大时间性态，在外力项ｆ（ｘ）（Ｌ２（Ｒ２））２而不需要对ｆ（ｘ）作任何加权限制的条件下，证明了线性阻尼Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程的全局吸引子的存在性，并给出了其Ｈａｕｓｄｏｒｆｆ及Ｆｒａｃｔａｌ维数估计．
The long time behaviors of Navier-Stokes equations with linear dampness on the whole two-dimensional space were investigated. The existence of global attractor of the equations was proved under only condition f(x) E (L2(R2))2. Moreover, the upper bounds of Hausdorff and Fractal dimensions of the global attractor were given.
出处
《应用数学学报》
CSCD
北大核心
2000年第1期90-98,共9页
Acta Mathematicae Applicatae Sinica
基金
国家自然科学基金
关键词
线性阻尼
全局吸引子
Fractal维数
N-S方程
估计
Linear dampness, Navier-Stokes equations, Global attractor, Hausdorff and Fractal dimensions
