华东师范大学学报(自然科学版) ›› 2010, Vol. 2010 ›› Issue (5): 56-66.

• 应用数学与基础数学 • 上一篇    下一篇

一类修正Navier-Stokes方程解的大时间行为

冯珍珍1, 吴 珞2   

  1. 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
  • 收稿日期:2010-04-01 修回日期:2010-07-01 出版日期:2010-09-25 发布日期:2010-09-25
  • 通讯作者: 冯珍珍

Large time behavior of a solution for the modified Navier-Stokes equations

FENG Zhen-zhen1, WU Luo2   

  1. 1. Interdisciplinary Research Centre, Shanghai Normal University, Shanghai 200234, China; 2. School of Science, Shanghai Second Polytechnic University, Shanghai 201209, China.
  • Received:2010-04-01 Revised:2010-07-01 Online:2010-09-25 Published:2010-09-25
  • Contact: FENG Zhen-zhen

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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.

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

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.

Key words: large time behavior, decay rate, modified Navier-Stokes equations, large time behavior, decay rate

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