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中文摘要：
基于层化的理论，为一架赤道的贝它飞机上的线性浅水的方程的起始的价值问题的 well-posedness 被讨论。Thesufficient 和为方程的本地答案的存在和唯一的必要条件被介绍，为方程的正式答案的存在条件也被给。为超上的 Cauchy 问题 { t = 0 } ，本地分析答案被得出，一种特殊情况被讨论。最后，一个例子被用来解释提出病的问题的正式解决方案的变化。
英文摘要：
Based on the theory of stratification, the well-posedness of the initial value problem for the linear shallow-water equations on an equatorial beta-plane was discussed. The sufficient and necessary conditions of the existence and uniqueness for the local solution of the equations were presented and the existence conditions for formal solutions of the equations vere also given. For the Cauchy problem on the hyper-plane {t = O}, the local analytic solution were worked out and a special case was discussed. Finally, an example was used to explain the variety of formal solutions for the ill-posed problem.
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