Ladyzhenskaya流体力学方程组的确定模与确定结点个数估计

数学物理学报 ›› 2018, Vol. 38 ›› Issue (1): 71-82.

Ladyzhenskaya流体力学方程组的确定模与确定结点个数估计

张明书¹, 朱泽奇², 赵才地¹

1. 温州大学数学与信息科学数学学院浙江温州 325035;
2. 中国科学院武汉岩土力学研究所武汉 430071

收稿日期:2016-12-14 修回日期:2017-04-10 出版日期:2018-02-26 发布日期:2018-02-26
通讯作者: 赵才地 E-mail:zhaocaidi2013@163.com
基金资助:
国家自然科学基金（11271290，51279202）和浙江省自然科学基金（LY17A010011）

Determining Modes and Determining Nodes to the Fluid Flow of Ladyzhenskaya Model

Zhang Mingshu¹, Zhu Zheqi², Zhao Caidi¹

1. Department of Mathematics and Information Science, Wenzhou University, Zhejiang Wenzhou, 325035;
2. State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071

Received:2016-12-14 Revised:2017-04-10 Online:2018-02-26 Published:2018-02-26
Supported by:
Supported by the NSFC (11271290, 51279202) and the Natural Science Foundation of Zhejiang Province (LY17A010011)

摘要/Abstract

摘要： 论文给出了二维有界区域上Ladyzhenskaya流体力学方程组的确定模与确定结点的个数估计.结果表明若该方程组的任意两个弱解的前有限个傅立叶模有相同的渐近行为，则这两个解就具有相同的渐近行为；若该方程组的任意两个强解在有限个空间中的点上有相同的渐近行为，则这两个解几乎在整个空间上具有相同的渐近行为.

关键词: Ladyzhenskaya流体力学方程组, 确定模, 确定结点, 渐近行为

Abstract: This article estimates the finite number of determining modes and determining nodes for the fluid flow of Ladyzhenskaya model on two-dimensional bounded smooth domains. The finite number of determining modes implies that the solutions of the addressed fluids are determined completely by their first finite number of Fourier modes. The determining nodes reveals that whenever two different solutions of the fluid have the same asymptotic behavior at finite number of points in the physical space, then they also possess the same asymptotic behavior at almost everywhere points of the physical space.

Key words: Ladyzhenskaya model, Determining modes, Determining nodes, Asymptotic behavior

中图分类号:

O212.62

张明书, 朱泽奇, 赵才地. Ladyzhenskaya流体力学方程组的确定模与确定结点个数估计[J]. 数学物理学报, 2018, 38(1): 71-82.

Zhang Mingshu, Zhu Zheqi, Zhao Caidi. Determining Modes and Determining Nodes to the Fluid Flow of Ladyzhenskaya Model[J]. Acta mathematica scientia,Series A, 2018, 38(1): 71-82.

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