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 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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References
Shih Weihui. Solutions analytiques de quelques equations aux derives partielles en mecanique des fluids[M]. Paris: Hermann, 1992, 93–114.
Shi Weihui, Chen Daduan, He Youhua. The foundations of stratification theory and partial differential equation[M]. Shanghai: Shanghai University Press, 2001, 10–152, 134–186 (in Chinese).
Zeng Qingcun. The foundation of mathematic physics of NWP [M]. Vol.1, Beijing: Science Press, 1979, 1–22 (in Chinese).
Liu Shishi, Liu Shida. Atmospheric dynamics[M]. Beijing: Beijing University Press, 1999, 1–33 (in Chinese).
Lü Meizhong, Hou Zhiming, Zhou Yi. Dynamic meteorology[M]. Beijing: Meteorological Press, 2004, 169–173 (in Chinese).
Shih Weishu. Stratifications et equations aux derivees partielles, singularities of maps, and applications to differential equations[M]. Collections TRAVAUX EN COURS 54, Paris: Hermann, 1997, 95–124.
Landau L, Lifchitz E. Mecanique des fluides[M]. Moscou: Editions Mir, 1971, 31–122.
Zhang Yuling. Introduction to meso-scale atmospheric dynamics[M]. Beijing: Meteorological Press, 1999, 10–16 (in Chinese).
Yu Zhihao, Yang Dasheng, He Haiyan, et al. Geophysical fluid mechanics[M]. Beijing: Meteorological Press, 1996, 37–128 (in Chinese).
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(Communicated by ZHOU Zhe-wei)
Project supported by the National Natural Science Foundation of China (Nos.40175014, 90411006) and the Science Foundation of Shanghai Municipal Commission of Science and Technology (No.02DJ14032)
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Shi, Wh., Wang, Yp. Impact of singularity of Navier-Stokes equation upon atmospheric motion equations. Appl Math Mech 28, 689–693 (2007). https://doi.org/10.1007/s10483-007-0513-1
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DOI: https://doi.org/10.1007/s10483-007-0513-1
Key words
- equations of atmospheric motion
- Navier-Stokes equation
- Boussinesq approximation
- stability
- singular equation