等离子体物理和大气海洋动力学中某些偏微分方程的研究

本项目主要研究等离子体物理和大气海洋动力学中某些偏微分方程(包括分数阶偏微分方程)。我们的研究内容主要分为两方面：等离子体物理中一些非线性偏微分方程的适定性和等离子体中波的稳定性理论；大气海洋动力学中一些数学模型的定性理论以及大气、海洋中波的稳定性理论。等离子体物理和大气海洋动力学中偏微分方程的研究，是一个等离子体物理、流体动力学、偏微分方程、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 some partial differential equations (including some fractional PDE)in Plasma Physics and the Atmosphere-Ocean dynamics is a cross-subject, based on Plasma Physics, Fluid Dynamics, PDE, Dynamical Systems and the Soliton Theory. Firstly, we consider the global well-posedness theory for some PDEs in the theoretical study of Plasma Physics and the stability theory of some waves in plasmas. Secondly, we study the mathematical models in the Atmosphere-Ocean Dynamics and the stability and instability of waves in the atmosphere and oceans.The subject is meaningful and has some application in the understanding the mechanism of the motion of plasmas, the atmosphere and oceans.