大气运动基本方程组的解析解  

Analytical Solution of the Basic Equations Set of Atmospheric Motion

作　　者：施惟慧[1] 沈春[2] 王曰朋[3] 周哲玮 

机构地区：[1]上海大学数学系,上海200444 [2]上海市应用数学和力学研究所 [3]南京信息工程大学数学系,南京210044

出　　处：《应用数学和力学》2007年第3期349-358,共10页Applied Mathematics and Mechanics

基　　金：国家自然科学基金"十五"重大研究计划资助项目(90411006)

摘　　要：在已知大气运动基本方程于光滑函数类中具有最好的稳定性前提下,讨论了它的局部解的解空间构造.根据它的解空间构造,分析了这个方程具有代表性和应用性的第三初值问题,在解析函数类中给出了适定的第三初值问题的解析解的计算方法以及具体的关系表达式,在局部解意义下完整的解决了这一点初值问题的解析解所涉及的理论与计算问题.指出其它类型定解问题都可以仿照文中的计算方法和步骤,求出所需要的稳定的解析解.In the smooth function classes, the basic equations set of atmospheric motion possesses the best stability, under this condition, its structure of solution space for local analytical solution was discussed, by which the third-class initial value problem with typicality and application was also analyzed. And in the analytic function classes, the calculational method and concrete expressions of analytical solution about the well-posed initial value problem of the third kind were given. In the meaning of local solution, near a appointed point, the relevant theoretical and computational problems about analytical solution of initial value problem were solved completely. Meanwhile, it is pointed out here that, with other types of problems for determining solution, the computational method and process of their stable analytical solution can be obtained in a similar way if needed.

关 键 词：大气运动基本方程组 解空间构造 解析解 

分 类 号：O175.29[理学—数学]