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

1.
Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China;

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

[1]	SHIH Wei-hui.Solutions Analytiques de Quelques Equations aux Derives Partielles en Mecanique des Fluids[M].Paris,France: Hermann, 1992, 93-114.
[2]	施惟慧,陈达段,何幼桦.分层理论与非线性偏微分方程基础[M].上海:上海大学出版社，2001,10-152, 134-186.
[3]	曾庆存.数值天气预报的数学物理基础（第一卷）[M]. 北京:科学出版社，1979,1-22.
[4]	刘式适,刘式达.大气动力学[M].北京:北京大学出版社，1999,1-33.
[5]	吕美仲,侯志明,周毅.动力气象学[M].北京:气象出版社，2004, 169-173.
[6]	SHIH Wei-shu.Stratifications et Equations aux Derivees Partie-lles, Singularities of Maps and Applications to Differential Equations[M].Paris,France:Hermann,Collections TRAVAUX EN COURS,1997,54:95-124.
[7]	Landau L,Lifchitz E.Mecanique des Fluides[M].Moscou:Editions Mir Moscou, 1971, 31-122.
[8]	张玉玲.中尺度大气动力学引论[M].北京:气象出版社，1999,10-16.
[9]	余志豪，杨大升，贺海晏，等.地球物理流体力学[M].北京:气象出版社，1996,37-128.