利用泛函理论，建立关于大气系统Navier-Stokes动力学方程组各变量的Hilbert空间，并将该方程组化为一个Hilbert空间中的非线性算子方程。在此基础上，为考虑方程的整体特征，通过必要的简化，将一个本质为欠定的偏微分方程组化为一个关于广义能量的非线性偏微分方程。由于该偏微分方程的非线性性质，试图考虑其弱解的存在性。经分析发现，在外源强迫为已知或固定的情况下，如果在湍流闭合过程，使关于广义能量方程的非线性项系数具有强椭圆性质，那么根据连续正规算子方程的投影解法，可以确定该非线性偏微分方程具有投影解，且投影解收敛于弱解，从而得出广义能量弱解的存在性。对于大气运动而言，其能量守恒是重要的，因此，最后对广义能量守恒进行了讨论，得到广义能量守恒的条件 。

The equations are reduced to nonlinear operator equations of Hilbert space by using functional theory, based on each variable Hilbert space of the general system of atmospheric Navier-Stokes dynamics equations. Thereby, considered the equation for the overall characteristics on this basis, using necessary simplification, the underdetermined partial differential equations are reduced to nonlinear partial differential equations about generalized energy. Because of the nonlinear properties of the partial differential equations, the existence of weak solutions is attempted to consider. According to the analysis, in the turbulent closure process, if the nonlinear coefficient of the generalized energy equation has characteristics of strongly elliptic, according to the projection method of the continuous normal operator equations, that nonlinear partial differential equations of generalized energy has a projection determined, which approach the weak solution, while the external force is known or fixed. In last, the existence of weak solutions for generalized energy is obtained. On the movement of atmosphere, its energy conservation is important. Therefore, conserve-ation of generalized energy is discussed. And the conditions of reaching the conservation of general-ized energy is obtained in the last of this paper.