大气海洋方程是天气预报和大气湍流的基本模型，是最先进的环流模式的分析核心。由于地球大气系统的复杂的多尺度性，在大气和洋流的演化过程中出现了很多的不确定性，为了深入的理解这些物理现象，大气海洋学家们非常重视随机方法的引入。本项目从随机数学的角度研究大气海洋方程的正则性以及渐近性质。具体来说，我们的研究内容包括：1）三维随机大气海洋方程的长时间动力学行为；2）随机初始值的可乘噪声驱动的三维大气海洋方程的整体适定性；3）水平耗散（垂直耗散缺失）的随机大气海洋方程整体适定性；4）分数布朗运动驱动的3维随机大气海洋方程吸引子的鲁棒性以及渐近性；5）三维随机大气海洋方程的噪声逼近问题；6）退化噪声驱动的三维随机大气海洋方程的遍历性。

The primitive equations (PEs) of the ocean and atmosphere dynamics are a basic model in the study of large scale oceanic and atmospheric dynamics. These systems form the analytical core of the most advanced general circulation models. In view of the complex multi-scale nature of the earth’s climate system, many uncertainties appear that should be accounted for in the basic dynamical models of atmospheric and oceanic processes. In the climate community stochastic methods have come into extensive use in this connection. For this reason the present project focuses on the study of regularity and asymptotic behavior for the stochastic primitive equations of the ocean and atmosphere dynamics. More concretely, we will study: 1) Dynamics of stochastic 3D PEs ; 2) Global well-posedness of stochastic 3D PEs driven by multiplicative noise with random initial data; 3) Global well-posedness of stochastic 3D PEs with horizontal eddy diffusivity; 4) Robustness and asymptotic behavior of random attractor for stochastic 3D PEs driven by fractional Brownian motion; 5) Approximation of stochastic 3D PEs; 6) Ergodicity of stochastic 3D PEs with degenerate noise.