Navier-Stokes方程的奇异性对大气运动方程组的影响

基金项目: 国家自然科学基金“十五”重大研究计划资助项目(90411006)

Impact of Singularity of Navier-Sokes Equation Upon the Atmospheric Motion Equations

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．
- 大气运动基本方程组 /
- Navier-Stokes方程 /
- Boussinesq近似 /
- 稳定性 /
- 奇异方程
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 Navie-rStokes equation,thereby,a principle to guarantee the stability of simplified equation is drawn in simplifying the basic system of equations.
- the basic system of equations of atmospheric motion /
- Navier-Stokes equation /
- Boussinesq approximation /
- stability /
- singular equation

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