The present paper takes advantage of the concept of dissipative measure-valued solutions to show the rigorous derivation of the Euler–Boussinesq (EB) system that has been successfully used in various meteorological models. In particular, we show that EB system can be obtained as a singular limit of the complete Euler system. We provide two types of result—firstly, we treat the case of well-prepared initial data for any sufficiently regular bounded domain. Secondly, we use the dispersive estimates for acoustic equation to tackle the case of the ill-prepared initial data on an unbounded exterior domain.

中文翻译：

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完整的欧拉系统的层次低

本文利用耗散量值解的概念来证明欧拉-布西涅斯（EB）系统的严格推导，该系统已成功用于各种气象模型中。特别是，我们表明，可以将EB系统作为完整Euler系统的奇异极限来获得。我们提供两种类型的结果-首先，对于任何足够规则的有界域，我们都要处理准备充分的初始数据。其次，我们使用声学方程的色散估计来解决无界外部域上原始数据准备不充分的情况。