关于海洋动力学中二维的大尺度原始方程组(Ⅰ)  

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

作　　者：黄代文[1] 郭柏灵[1] 

机构地区：[1]北京应用物理与计算数学研究所

出　　处：《应用数学和力学》2007年第5期521-531,共11页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(重点)资助项目(90511009)

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.The initial boundary value problem for the two-dimensional primitive equations of scale oceanic motion in geophysics is considered. It was assumed that the depth of the ocean is a positive constant. First,ff the initial data are square integrable, then, by Fadeo-Galerkin method, the existence of the global weak sohctions for the problem was obtained. Second, ff 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.

关 键 词：海洋的原始方程组 整体弱强解 存在性 唯一性 

分 类 号：O175[理学—数学]