地球物理流体动力学中的一些方程研究

本项目拟研究地球物理流体动力学（主要研究大尺度大气、海洋运动）中一些重要方程的数学理论。主要研究内容分为两方面：一，研究一些含有随机因素作用的长期天气预报、海洋环流数值预报和气候预测的数学模型，例如带退化噪声的三维大气和海洋原始方程组；二，研究大尺度大气、海洋动力学中一些特解的稳定性和不稳定性问题，例如二维和三维准地转方程的一些特殊解（例如一些正压流和斜压流）、海洋非线性内波、Ekman流和Gill流等的稳定性和不稳定性。地球物理流体动力学中偏微分方程的数学理论是一个地球物理、流体动力学、偏微分方程、随机分析、动力系统和孤立子理论交叉的课题，具有重要理论价值和实际意义。

The study of mathematical theories for some equations in geophysical fluid dynamics is a cross-subject, based on Geophysics, Fluid Dynamics, Partial Differential Equations, Stochastic Analysis, Dynamical Systems and the Soliton Theory. Firstly, we consider the mathematical theories for some stochastic models in long-term weather forecast, oceanic circulation numerical forecast and climate prediction, including three-dimensiona primitive equations of the large-scale atmosphere and oceans with degenerate noises. Secondly, we study the stability and instability of some important special solutions in atmospheric and oceanic dynamics, for example, some special solutions of 2D and 3D quasi-geostrophic equations (including Barotropic Instability and Baroclinic Instability), and the stability and instability of nonlinear internal waves in oceans, Ekman flows and Gill flow.The subject is meaningful and has some application in the understanding the mechanism of the large-scale motion of the atmosphere and oceans.