本项目主要研究高维情形下具有部分耗散的两类不可压缩地球流体力学方程组：磁流体力学(MHD)方程组和Boussinesq方程组。MHD方程组来源于等离子体和电解质等导电流体，在天体物理和地球物理中有重要应用。Boussinesq方程组描述了大气和海洋中流体的运动，在天气预报等实际生活中有广泛的运用。. 本项目将着重研究这两类方程组解的整体正则性和稳定性：1)利用bootstrapping方法研究具有部分耗散的MHD方程组在背景磁场附近和Boussinesq方程组在平衡态附近的稳定性和大时间行为问题。2)利用Littlewood-Paley方法讨论具分数阶耗散MHD方程组和Boussinesq方程组弱解的整体存在性和唯一性。本项目的实施将使我们进一步理解这两类方程，并期望对于高维不可压缩流体力学方程组在整体适定性方面有更多更深入的理解。

This project focuses on two systems of incompressible equations from geophysical fluid dynamics with partial dissipation in multi-dimension: the magnetohydrodynamic (MHD) equations and the Boussinesq equations. The MHD equations model electrically conducting fluids such as plasmas and electrolytes, and have many important applications in astrophysics and geophysics. The Boussinesq equations are among the most frequently used models for atmospheric and oceanic flows. Many practical applications such as weather forecasting are based on the Boussinesq equations.. This project intends to understand some of the most fundamental problems concerning these two systems. Our attention will be focused on the global regularity and stability problems. In particular, we will solve the stability and large-time behavior problem on the MHD equations with partial dissipation near a background magnetic field and the Boussinesq equations near the hydrodynamic equilibrium by bootstrapping argument. We will also examine the global existence and the uniqueness of weak solutions to the MHD equations and Boussinesq equations with fractional dissipation by Littlewood-Paley technique. This project will significantly enhance our understanding of the global-wellposedness of these two systems and multi-dimensional incompressible fluid.