| On two-dimensional large-scale primitive equations in oceanic dynamics （Ⅰ） |
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| 引用本文： | 黄代文,郭柏灵.On two-dimensional large-scale primitive equations in oceanic dynamics （Ⅰ）[J].应用数学和力学(英文版),2007,28(5):581-592. |
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| 作者姓名： | 黄代文 郭柏灵 |
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| 作者单位： | Institute of Applied Physics and Computational Mathematics，Institute of Applied Physics and Computational Mathematics Beijing 100088，P. R. China Graduate School，China Academy of Engineering Physics，Beijing 100088，P. R. China，Beijing 100088，P. R. China |
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| 基金项目： | Project supported by the National Natural Science Foundation of China (No.90511009) |
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| 摘 要： | The initial boundary value problem for the two-dimensional primitive equations of large scale oceanic motion in geophysics is considered. It is assumed that the depth of the ocean is a positive constant. Firstly, if the initial data are square integrable, then by Fadeo-Galerkin method, the existence of the global weak solutions for the problem is obtained. Secondly, if the initial data and their vertical derivatives are all square integrable, then by Faedo-Galerkin method and anisotropic inequalities, the existerce and uniqueness of the global weakly strong solution for the above initial boundary problem are obtained.
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| 关 键 词： | 二维大规模原始方程 海洋动力学 数学模型 大气-海洋耦合 |
| 收稿时间： | 2006-03-16 |
| 修稿时间： | 2007-03-05 |
On two-dimensional large-scale primitive equations in oceanic dynamics (I) |
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| Huang Dai-wen,Guo Bo-ling.On two-dimensional large-scale primitive equations in oceanic dynamics (I)[J].Applied Mathematics and Mechanics(English Edition),2007,28(5):581-592. |
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| Authors: | Huang Dai-wen Guo Bo-ling |
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| Institution: | Institute of Applied Physics and Computational Mathematics, Beijing 100088, P. R. China;Graduate School, China Academy of Engineering Physics, Beijing 100088, P. R. China |
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| Abstract: | The initial boundary value problem for the two-dimensional primitive equations of large scale oceanic motion in geophysics is considered. It is assumed that the depth of the ocean is a positive constant. Firstly, if the initial data are square integrable, then by Fadeo-Galerkin method, the existence of the global weak solutions for the problem is obtained. Secondly, if the initial data and their vertical derivatives are all square integrable, then by Faedo-Galerkin method and anisotropic inequalities, the existerce and uniqueness of the global weakly strong solution for the above initial boundary problem are obtained. |
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| Keywords: | primitive equations of the ocean global weakly strong solution existence uniqueness |
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