| 三维Navier-Stokes方程的正则性准则 |
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| 引用本文： | 罗兰,张辉.三维Navier-Stokes方程的正则性准则[J].湖南科技大学学报(自然科学版),2012,27(1):126-128. |
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| 作者姓名： | 罗兰 张辉 |
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| 作者单位： | 1. 广州大学数学与信息科学学院,数学与交叉科学广东普通高校重点实验室,广东广州510006
2. 湘潭大学数学与信息科学学院,湖南湘潭,411201 |
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| 基金项目： | 国家自然科学基金项目资助(11126021) |
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| 摘 要： | 考察三维不可压Navier-Stokes方程的弱解正则性问题.基于Holder不等式和速度场的不可压缩性质,通过对速度向量的部分分量及相关导数的估计,得到了一个新的关于Leray-Hopf弱解的正则性准则的结果.在速度向量的部分分量及相关导数满足适当的条件下,三维不可压Navier-Stokes方程的弱解是整体正则的.
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| 关 键 词： | Navier-Stokes方程 Leray-Hopf弱解 正则性准则 |
The regularity criterion for the 3D Navier- Stokes equations |
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| LUO Lan
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ZHANG Hui.The regularity criterion for the 3D Navier- Stokes equations[J].Journal of Hunan University of Science & Technology(Natural Science Editon),2012,27(1):126-128. |
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| Authors: | LUO Lan ZHANG Hui |
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| Institution: | 1.School of Mathematics and Information Science,Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes,Guangzhou University,Guangzhou 510006,China; 2.School of Mathematics and Information Science,Xiangtan University,Xiangtan 411201,China) |
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| Abstract: | The global regularity problem of 3-dimensional Navier-Stokes equations was investigated.By using the Holder inequality and the divergence free condition,a regularity criterion for the 3-dimensional Navier-Stokes equations was obtained based on estimating some derivatives of the two components of the velocity.It shows that the weak solutions is global regular if some assumptions on some derivatives of the two components of the velocity were satisfied. |
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| Keywords: | Navier-Stokes equaitons Leray-Hopf weak solution regularity criterion |
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