The primitive equations on the large scale ocean under the small depth hypothesis
The primitive equations on the large scale ocean under the small depth hypothesis
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DOI：
10.3934/dcds.2003.9.97
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发表时间：
2002-11
影响因子：
1.1
通讯作者：
Changbing Hu;R. Temam;M. Ziane
中科院分区：
文献类型：
--
作者：
Changbing Hu;R. Temam;M. Ziane
本文研究了小深度假设下大尺度海洋原始方程强解的整体存在性。小深度假设意味着海洋所占据的区域$M\vareps $是一个薄区域，其厚度参数$\vareps $是垂直尺度和水平尺度之间的纵横比。使用和推广[23]，[24]中开发的方法，我们建立了初始数据和体积和边界'力'的强解的整体存在性，它们属于各自相空间中的大集，只要$\vareps $足够小。我们的PE的存在性结果的证明是基于精确估计的依赖性的一些经典常数上的厚度$\varepsilon$的域。结果扩展到大气或海洋与大气耦合或其他相关边界条件将出现在其他地方。
In this article we study the global existence of strong solutions of the Primitive Equations (PEs) for the large scale ocean under the small depth hypothesis. The small depth hypothesis implies that the domain $M_\varepsilon$ occupied by the ocean is a thin domain, its thickness parameter $\varepsilon$ is the aspect ratio between its vertical and horizontal scales. Using and generalizing the methods developed in [23], [24], we establish the global existence of strong solutions for initial data and volume and boundary 'forces', which belong to large sets in their respective phase spaces, provided $\varepsilon$ is sufficiently small. Our proof of the existence results for the PEs is based on precise estimates of the dependence of a number of classical constants on the thickness $\varepsilon$ of the domain. The extension of the results to the atmosphere or the coupled ocean and atmosphere or to other relevant boundary conditions will appear elsewhere.