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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
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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