New Developments on Existence and Uniqueness of Solutions to Some Models in Atmospheric Dynamics

Mu Mu; Zeng Qingcun

doi:10.1007/BF02919262

Impact Factor: 5.8

Volume 8 Issue 4

Oct. 1991

Article Contents

Article > ADVANCES IN ATMOSPHERIC SCIENCES > 1991 > 8(4): 383-398

New Developments on Existence and Uniqueness of Solutions to Some Models in Atmospheric Dynamics

Mu Mu,
Zeng Qingcun

1.
LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, 100080,LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, 100080

Mu Mu,
Zeng Qingcun

doi: 10.1007/BF02919262

Abstract
References
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Abstract:
This survey is concerned with the new developments on existence and uniqueness of solutions of some basic mod-els in atmospheric dynamics, such as two-and three-dimensional quasi-geostrophic models and three-dimensional balanced model. The main aim of this paper is to introduce some results about the global and local (with respect to time) existence of solutions given by the authors in recent years, but others' important contributions and the literature on this subject are also quoted. We discuss briefly the relationships among the existence and uniqueness, physical in-stability and computational instability. In the appendixes, some key mathematical techniques in obtaining our results are presented, which are of vital importance to other problems in geophysical fluid dynamics as well.
References

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Manuscript History

Manuscript received: 10 October 1991

Manuscript revised: 10 October 1991

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

New Developments on Existence and Uniqueness of Solutions to Some Models in Atmospheric Dynamics

Mu Mu,
Zeng Qingcun

1. LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, 100080,LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, 100080

Manuscript received: 1991-10-10
Manuscript revised: 1991-10-10

Abstract: This survey is concerned with the new developments on existence and uniqueness of solutions of some basic mod-els in atmospheric dynamics, such as two-and three-dimensional quasi-geostrophic models and three-dimensional balanced model. The main aim of this paper is to introduce some results about the global and local (with respect to time) existence of solutions given by the authors in recent years, but others' important contributions and the literature on this subject are also quoted. We discuss briefly the relationships among the existence and uniqueness, physical in-stability and computational instability. In the appendixes, some key mathematical techniques in obtaining our results are presented, which are of vital importance to other problems in geophysical fluid dynamics as well.