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This paper is devoted to considering the three-dimensional viscous primitive equations of the large-scale atmosphere. First, we prove the global well-posedness for the primitive equations with weaker initial data than that in [11]. Second, we obtain the existence of smooth solutions to the equations. Moreover, we obtain the compact global attractor in V for the dynamical system generated by the primitive equations of large-scale atmosphere, which improves the result of [11].  相似文献   
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关于海洋动力学中二维的大尺度原始方程组(Ⅱ)   总被引:1,自引:1,他引:0  
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.这里海底的深度是正的,但不一定为常数.应用Faedo-Galerkin方法和各向异性不等式,得到上述初边值问题的整体弱强解和整体强解的存在、唯一性.并且通过研究解的渐近行为,证明了能量随时间是指数衰减的.  相似文献   
3.
We consider the two-dimensional stochastic quasi-geostrophic equation ■=1/(R_e)△~2■-r/2△■ f(x,y,t)(1.1) on a regular bounded open domain D ■,where ■ is the stream function,F Froude Number (F≈O(1)),R_e Reynolds number(R_e■10~2),β_0 a positive constant(β_0≈O(10~(-1)),r the Ekman dissipation constant(r≈o(1)),the external forcing term f(x,y,t)=-(dW)/(dt)(the definition of W will be given later)a Gaussian random field,white noise in time,subject to the restrictions  相似文献   
4.
黄代文 《数学进展》2007,36(1):119-121
We consider the two-dimensional stochastic quasi-geostrophic equation[12p.234,13]((Э)/(Э)t+(Э)ψ/(Э)x(Э)/(Э)y-(Э)ψ/(Э)y(Э)/(Э)x)(△ψ-Fψ+β0y)=1/Re△2ψ-r/2△ψ+f(x,y,t) (1.1)on a regular bounded open domain D (С) R2,where ψis the stream function,F Froude Number (F≈O(1)),Re Reynolds number(Re≥102),β0a Positive constant(β0≈O(10-1)),r the Ekman dissipation constant(r≈O(1)),the external forcing term f(x,y,t)=-dW/dt(the definition of W will be given later)a Gaussian random field,white noise in time,subject to the restrictions imposed below.  相似文献   
5.
关于海洋动力学中二维的大尺度原始方程组(Ⅰ)   总被引:1,自引:1,他引:0  
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.  相似文献   
6.
The initial boundary value problem for the two-dimensional primitive equations of largescale oceanic motion in geophysics is considered sequetially. Here the depth of the ocean is positive but not always a constant. By Faedo-Galerkin method and anisotropic inequalities, the existence and uniqueness of the global weakly strong solution and global strong solution for the problem are obtained. Moreover, by studying the asymptotic behavior of solutions for the above problem, the energy is exponential decay with time is proved.  相似文献   
7.
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.  相似文献   
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