| Navier-Stokes方程的奇异性对大气运动方程组的影响 |
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| 引用本文： | 施惟慧,王曰朋. Navier-Stokes方程的奇异性对大气运动方程组的影响[J]. 应用数学和力学, 2007, 28(5): 614-618 |
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| 作者姓名： | 施惟慧 王曰朋 |
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| 作者单位： | 上海大学 数学系,上海 200444;2.南京信息工程大学 数学系, 南京 210044 |
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| 摘 要： | 综述了大气运动基本方程组在光滑函数类中的稳定性和Navier-Stokes方程的不稳定性的若干结论．在此基础上，以大气运动方程组的Boussinesq近似为例，阐述了Navier-Stokes方程的不稳定性导致的大气运动基本方程组的某些简化模式的不稳定性，从而得到在简化基本方程过程中应该遵守的一个原则，以保证简化方程的稳定性．
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| 关 键 词： | 大气运动基本方程组 Navier-Stokes方程 Boussinesq近似 稳定性 奇异方程 |
| 文章编号： | 1000-0887（2007）05-0614-05 |
| 收稿时间： | 2005-01-20 |
| 修稿时间： | 2005-01-20 |
Impact of Singularity of Navier-Sokes Equation Upon the Atmospheric Motion Equations |
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| SHI Wei-hui,WANG Yue-peng. Impact of Singularity of Navier-Sokes Equation Upon the Atmospheric Motion Equations[J]. Applied Mathematics and Mechanics, 2007, 28(5): 614-618 |
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| Authors: | SHI Wei-hui WANG Yue-peng |
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| Affiliation: | Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China; |
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| Abstract: | Some conclusions about the smooth function classes stability for the basic system of equations of atmospheric motion and instability for Navier-Stokes equation are summarized.On the basis of this,by taking the basic system of equations of atmospheric motion via Boussinesq approximation as an example to explain in detail that the instability about some simplified models of the basic system of equations for atmospheric motion is caused by the instability of Navier-Stokes equation,thereby,a principle to guarantee the stability of simplified equation is drawn in simplifying the basic system of equations. |
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| Keywords: | the basic system of equations of atmospheric motion Navier-Stokes equation Boussinesq approximation stability singular equation |
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