Impact of singularity of Navier-Stokes equation upon atmospheric motion equations  

作　　者：施惟慧 王曰朋 

机构地区：[1]Department of Mathematics,Shanghai University [2]Department of Mathematics,Nanjing University of Information Science & Technology

出　　处：《Applied Mathematics and Mechanics(English Edition)》2007年第5期689-693,共5页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (Nos.40175014, 90411006);the Science Foundation of Shanghai Municipal Commission of Science and Technology(No.02DJ14032)

摘　　要：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 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.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 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.

关 键 词：equations of atmospheric approximation stability singular equation motion Navier-Stokes equation BOUSSINESQ 

分 类 号：P432[天文地球—大气科学及气象学] O175.29[理学—数学]