磁流体力学是研究导电流体和磁场相互作用及变化规律的学科，在天体物理，热核反应与工业等领域中有诸多应用。本项目拟围绕以下几个方面开展: (1) 利用混合型有限元-有限体积数值方法构造三维等熵可压缩磁流体力学方程组的测度值解，建立相对能量不等式并研究弱强唯一性，即只要测度值解与光滑解由同一光滑初始值决定，则在光滑解的生命跨度内两者恒同; (2) 基于相对能量不等式和色散估计，在测度值解的框架下研究磁流体力学方程组相关的奇异极限问题，如粘性消失极限、低马赫数极限、磁扩散消失极限; (3) 考虑水平方向运动而磁场仅在垂直方向作用的可压缩磁流体模型，利用经典的Lions-Feireisl方法与可压缩两相流中“变量约化”的新技术研究其弱解的整体存在性。本项目拟在数学上严格证明磁场在磁流体运动中所起的稳定性作用，并对相应的物理现象有更好的认识。

Magnetohydrodynamics (MHD) is concerned with the time evolution and mutual interactions between electrically conducting fluids and magnetic field. It is widely applied in astrophysics, thermonuclear reactions and industry, among others. This project is concerned with the following: (1) to construct measure-valued solutions to 3D isentropic compressible MHD system through a mixed finite element-finite volume scheme, establish the relative energy inequality and study weak-strong uniqueness principle, namely a measure-valued solution coincides with a classical one as long as the latter exists and emanate from the same initial data; (2) based on the relative energy inequality and dispersive estimates, to study singular limits in the framework of measure-valued solutions, such as vanishing viscosity limit, low Mach number limit and vanishing resistivity coefficient; (3) consider the compressible MHD model of motion in the plane and the action of magnetic field only in the vertical direction, to study existence of global-in-time weak solutions by the classical Lions-Feireisl method and the new technique of “variable reduction”.The purpose of this project is to give mathematically rigorous evidences of stabilization effect of magnetic field and reach a better understanding for corresponding physical phenomena.