| 关于海洋动力学中二维的大尺度原始方程组(Ⅰ) |
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| 引用本文： | 黄代文,郭柏灵.关于海洋动力学中二维的大尺度原始方程组(Ⅰ)[J].应用数学和力学,2007,28(5):521-531. |
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| 作者姓名： | 黄代文 郭柏灵 |
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| 作者单位： | 1. 北京应用物理与计算数学研究所,北京,100088;中国工程物理研究所,研究生部,北京,100088
2. 北京应用物理与计算数学研究所,北京,100088 |
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| 摘 要： | 考虑地球物理学中大尺度海洋运动的二维原始方程组的初边值问题.先假定海洋的深度为正的常数.首先,当初始数据是平方可积时,应用Faedo-Galerkin方法,得到了这一问题整体弱解的存在性.其次,当初始数据及其它们关于垂直方向的导数均为平方可积时,应用Faedo-Galerkin方法和各向异性不等式,得到了上述初边值问题的整体弱强解的存在、唯一性.
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| 关 键 词： | 海洋的原始方程组 整体弱强解 存在性 唯一性 |
| 文章编号： | 1000-0887（2007）05-0521-11 |
| 修稿时间： | 2006-03-06 |
On the Two-Dimensional Large-Scale Primitive Equations in Oceanic Dynamics ( Ⅰ ) |
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| HUANG Dai-wen,GUO Bo-ling.On the Two-Dimensional Large-Scale Primitive Equations in Oceanic Dynamics ( Ⅰ )[J].Applied Mathematics and Mechanics,2007,28(5):521-531. |
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| Authors: | HUANG Dai-wen GUO Bo-ling |
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| Institution: | Institute of Applied Physics and Computational Mathematics, 2. Graduate School, China Academy of Engineering Physics 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 was assumed that the depth of the ocean is a positive constant.First,if the initial data are square integrable,then,by Fadeo-Galerkin method,the existence of the global weak sohctions for the problem was obtained.Second,if the initial data and their vertical derivatives are all square integrable,then by Faedo-Galerkin method and anisotropit inequahites,the existerce and uniqueness of the global weakly strong solution for the above initial boundary problem was obtained. |
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| Keywords: | primitive equations of the ocean global weakly strong solution existence uniqueness |
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