无界区域上具线性阻尼的二维 Navier-Stokes 方程的拉回吸引子 |
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引用本文: | 王小虎,李树勇. 无界区域上具线性阻尼的二维 Navier-Stokes 方程的拉回吸引子[J]. 数学物理学报(A辑), 2009, 29(4): 873-881 |
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作者姓名: | 王小虎 李树勇 |
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作者单位: | 王小虎(四川大学数学学院,成都,610064);李树勇(四川师范大学数学与软件科学学院,成都,610066) |
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摘 要: | 该文首先介绍拉回渐近紧非自治动力系统的概念, 给出非自治动力系统拉回吸引子存在定理. 最后证明了无界区域上具线性阻尼的二维Navier-Stokes 方程的拉回吸引子的存在性, 并给出了其Fractal维数估计.
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关 键 词: | 渐近紧 过程 非自治 线性阻尼 拉回吸引子 |
收稿时间: | 2008-01-08 |
修稿时间: | 2009-02-23 |
Pullback Attractors for Non-autonomous 2D Navier-Stokes Equations with Linear Dampness in Some Unbounded Domains |
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Affiliation: | (1. Department of Mathematics, Sichuan University, Chengdu 610064, 2. Department of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066) |
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Abstract: | In this paper, the concept of pullback asymptotically compact non-autonomous dynamical system is firstly introduced. Then, a result ensuring the existence of a pullback attractor for a non-autonomous dynamical system is given. Finally, the existence of a pullback attractor for a non-autonomous 2D Navier-Stokes equation with linear dampness in some unbounded domains is proved. Moreover, the upper bounds of Fractal dimension of the pullback attractor is estimated. |
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Keywords: | Asymptotic compactnesszz Processzz Non-autonomouszz Linear dampnesszz Pullback attractorzz |
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