On the Two-Dimensional Large-Scale Primitive Equations in Oceanic Dynamics (Ⅰ)
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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.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.
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Key words:
- primitive equations of the ocean /
- global weakly strong solution /
- existence /
- uniqueness
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