关于海洋动力学中二维的大尺度原始方程组(Ⅰ)

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)

黄代文^1,2,
郭柏灵¹

1.
北京应用物理与计算数学研究所,北京 100088;2.中国工程物理研究所研究生部,北京 100088

基金项目: 国家自然科学基金(重点)资助项目(90511009)

详细信息

作者简介:
黄代文(1977- ),男,福建云霄人,博士(联系人.Tel:+86-10-62014411-2645;E-mail:hdw55@tom.com).

中图分类号: O175
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出版历程
- 收稿日期: 2006-03-06
- 修回日期: 2007-04-09
- 刊出日期: 2007-05-15

On the Two-Dimensional Large-Scale Primitive Equations in Oceanic Dynamics (Ⅰ)

HUANG Dai-wen^1,2,
GUO Bo-ling¹

1.
Institute of Applied Physics and Computational Mathematics, Beijing 100088, P. R. China;

摘要

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．
- 海洋的原始方程组 /
- 整体弱强解 /
- 存在性 /
- 唯一性
Abstract: The initial boundary value problem for the two-dimensional primitive equations of largescale 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.
- primitive equations of the ocean /
- global weakly strong solution /
- existence /
- uniqueness

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参考文献(14)

[1]	Lions J L, Teman R，Wang S.New formulations of the primitive equations of atmosphere and applications[J].Nonlinearity,1992,5:237-288. doi: 10.1088/0951-7715/5/2/001
[2]	Lions J L,Teman R，Wang S.On the equations of the large scale ocean[J].Nonlinearity,1992,5:1007-1053. doi: 10.1088/0951-7715/5/5/002
[3]	Lions J L,Teman R,Wang S.Models of the coupled atmosphere and ocean(CAO I)[J].Computational Mechanics Advance,1993,1:1-54.
[4]	Lions J L,Teman R,Wang S.Mathematical theory for the coupled atmosphere-ocean models(CAO Ⅲ)[J].J Math Pures Appl,1995,74:105-163.
[5]	Wang S.On the 2D model of large-scale atmosphic motion: well-posedness and attractors[J].Nonlinear Anal,TMA,1992,18:17-60. doi: 10.1016/0362-546X(92)90046-H
[6]	Bresch D,Guillén-Gonzlez F,Masmoudi N,et al.On the uniqueness for the two-dimensional primitive equations[J].Diff Int Equ,2003,16(1):77-94.
[7]	Bresch D,Kazhikhov A,Lemoine J.On the two-dimensional hydrostatic Navier-Stokes equations[J].SIAM J Math Anal,2004,36(3):796-814.
[8]	Guillén-Gonzlez F,Masmoudi N,Rodríguez-Bellido M A.Anisotropic estimates and strong solutions for the primitive equations[J].Diff Int Equ,2001,14(11):1381-1408.
[9]	Petcu M, Temam R,Wirosoetisno D.Existence and regularity results for the primitive equations in the two dimensions[J].Comm on Pure and Appl Anal,2004,3(1):115-131. doi: 10.3934/cpaa.2004.3.115
[10]	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(Ⅱ)[J].应用数学和力学，2007，28(5)：532-538.
[11]	Pedlosky J.Geophysical Fluid Dynamics[M].2nd Edition.Berhn/New York:Springer-Verlag,1987.
[12]	Washington W M,Parkinson C L.An Introduction to Three-Dimensional Climate Modelling[M].England:Oxford Univ Press,1986.
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关于海洋动力学中二维的大尺度原始方程组(Ⅰ)

作者简介:
黄代文(1977- ),男,福建云霄人,博士(联系人.Tel:+86-10-62014411-2645;E-mail:hdw55@tom.com).

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On the Two-Dimensional Large-Scale Primitive Equations in Oceanic Dynamics (Ⅰ)

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关于海洋动力学中二维的大尺度原始方程组(Ⅰ)

作者简介: 黄代文(1977- ),男,福建云霄人,博士(联系人.Tel:+86-10-62014411-2645;E-mail:hdw55@tom.com).

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出版历程

On the Two-Dimensional Large-Scale Primitive Equations in Oceanic Dynamics (Ⅰ)

计量

出版历程

目录

作者简介:
黄代文(1977- ),男,福建云霄人,博士(联系人.Tel:+86-10-62014411-2645;E-mail:hdw55@tom.com).