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Applied Mathematics and Mechanics (English Edition) ›› 2007, Vol. 28 ›› Issue (3): 385-385 .doi: https://doi.org/10.1007/s,10483-007-0311-x

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Analytical solution of basic equations set of atmospheric motion

施惟慧1;沈春2 3; 王曰朋4   

  1. 1. Department of Mathematics, Shanghai University,Shanghai 200444, P. R. China; 2. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University,Shanghai 200072, P. R. China;3. School of Mathematics and Information, Yantai Normal University, Yantai 264025,Shandong Province, P. R. China;4. Department of Mathematics, Nanjing University of Information Science Technology,Nanjing 210044, P. R. China
  • 收稿日期:2005-01-20 修回日期:2006-12-12 出版日期:2007-03-25 发布日期:2007-03-25

Analytical solution of basic equations set of atmospheric motion

SHI Wei-hui1; SHEN Chun2 3; WANG Yue-peng4   

  1. 施惟慧1;沈春2 3; 王曰朋4
  • Received:2005-01-20 Revised:2006-12-12 Online:2007-03-25 Published:2007-03-25

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摘要： On condition that the basic equations set of atmospheric motion possesses the best stability in the smooth function classes, the structure of solution space for local analytical solution is discussed, by which the third-class initial value problem with typicality and application is analyzed. The calculational method and concrete expressions of analytical solution about the well-posed initial value problem of the third kind are given in the analytic function classes. Near an appointed point, the relevant theoretical and computational problems about analytical solution of initial value problem are solved completely in the meaning of local solution. Moreover, for other type of problems for determining solution, the computational method and process of their stable analytical solution can be obtained in a similar way given in this paper.

关键词: basic equations set of atmospheric motion, structure of solution space, analytical solution

Abstract: On condition that the basic equations set of atmospheric motion possesses the best stability in the smooth function classes, the structure of solution space for local analytical solution is discussed, by which the third-class initial value problem with typicality and application is analyzed. The calculational method and concrete expressions of analytical solution about the well-posed initial value problem of the third kind are given in the analytic function classes. Near an appointed point, the relevant theoretical and computational problems about analytical solution of initial value problem are solved completely in the meaning of local solution. Moreover, for other type of problems for determining solution, the computational method and process of their stable analytical solution can be obtained in a similar way given in this paper.

Key words: basic equations set of atmospheric motion, structure of solution space, analytical solution

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