| 一类修正Navier-Stokes方程解的大时间行为 |
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| 引用本文： | 冯珍珍,吴珞.一类修正Navier-Stokes方程解的大时间行为[J].华东师范大学学报(自然科学版),2010,2010(5):56-66. |
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| 作者姓名： | 冯珍珍 吴珞 |
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| 作者单位： | 1. 上海师范大学跨学科研究中心,上海,200234
2. 上海第二工业大学理学院,上海,201209 |
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| 基金项目： | 上海市自然科学基金，上海市教育委员会科研创新项目 |
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| 摘 要： | O.A.Ladyzhenskaya于1966年放弃了速度梯度很小的限制,提出了一类描述三维非稳态不可压缩粘性流体运动规律的修正Navier-Stokes方程.本文研究有界区域上这一修正Navier-Stokes方程解的大时间行为,证明当外力为零时,解的衰减速度是精确的指数型.而且能量的涡度拟能当时间趋于无穷大时,其极限是Stokes算子的一个特征值.
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| 关 键 词： | 修正Navier-Stokes 大时间行为 衰减率 修正Navier-Stokes 大时间行为 衰减率 |
| 收稿时间： | 2010-4-1 |
| 修稿时间： | 2010-7-1 |
Large time behavior of a solution for the modified Navier-Stokes equations |
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| FENG Zhen-zhen,WU Luo.Large time behavior of a solution for the modified Navier-Stokes equations[J].Journal of East China Normal University(Natural Science),2010,2010(5):56-66. |
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| Authors: | FENG Zhen-zhen WU Luo |
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| Institution: | 1. Interdisciplinary Research Centre, Shanghai Normal University, Shanghai 200234, China;
2. School of Science, Shanghai Second Polytechnic University, Shanghai 201209, China. |
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| Abstract: | In 1966, O. A. Ladyzhenskaya proposed a kind of modified Navier-Stokes equations to describe the three-dimensional nonstationary flows of viscous incompressible fluids without assuming small gradients of the velocities. This paper considered large time behavior of a solution for the modified Navier-Stokes equations in a bounded domain and showed that decay of the solution is exactly of exponential type when force term is equal to zero.Moreover the ratio of the enstrophy over the energy has a limit as time tends to infinity, and the limit is an eigenvalue of the Stokes operator. |
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| Keywords: | modified Navier-Stokes equations large time behavior decay rate |
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