干的无粘大气环流方程组混合问题的适定性

上海大学学报(自然科学版)

干的无粘大气环流方程组混合问题的适定性

宋承燕，何幼桦

上海大学理学院，上海 200444

收稿日期:2006-10-17 修回日期:1900-01-01 出版日期:2007-12-20 发布日期:2007-12-20
通讯作者: 何幼桦

宋承燕，何幼桦

SONG Cheng-yan,HE You-hua

School of Sciences, Shanghai University, Shanghai 200444, China

Received:2006-10-17 Revised:1900-01-01 Online:2007-12-20 Published:2007-12-20
Contact: HE You-hua

摘要/Abstract

摘要：

该文针对干的无粘大气环流方程组的混合问题,讨论其底部边界的混合问题.所采用的分析方法是将该混合问题分解成两部分:一个纯Cauchy问题和一组积分表达式.首先证明了这样的分解与原问题同解,然后用分层方法讨论相应Cauchy问题的适定性，从而得到了原混合问题的适定的充要条件.最后给出了构造适定混合问题解析解的计算方法.

关键词: 大气环流方程, 分层理论, 混合问题, 适定性

Abstract:

The mixed problem with lower bound for dry inviscid atmospheric circulation equations is discussed. We decompose the problem into two parts: a pure Cauchy problem and a group of integration expressions. We show that such decomposition gives the same solution with the original problem, and discuss wellposedness of the Cauchy problem based on the stratification theory. A necessary and sufficient condition for wellposedness of the original mixed problem is then obtained. A method for obtaining an analytic solution to the wellposed mixed problem is given.

Key words: mixed problem, stratification theory, wellposedness

atmospheric circulation equation

宋承燕;何幼桦. 干的无粘大气环流方程组混合问题的适定性[J]. 上海大学学报(自然科学版).

SONG Cheng-yan;HE You-hua. 宋承燕，何幼桦[J]. Journal of Shanghai University（Natural Science Edition）.