磁流体力学方程组的渐近极限和适定性

磁流体力学主要研究电中性的导电流体在电磁场中的运动规律。本项目研究磁流体力学方程组的渐近极限和适定性。主要内容包括：有界区域上可压缩等熵和非等熵磁流体力学方程组的低Mach数极限问题，有界区域或半空间上具有Navier边界条件的可压缩等熵和非等熵磁流体力学方程组的粘性消失极限问题，有界区域上具有Navier边界条件的不可压缩磁流体力学方程组的粘性消失极限问题以及有界区域或半空间上的无磁扩散的可压缩和不可压缩磁流体力学方程组的小解的整体存在性问题等等。.. 上述研究内容不仅是国际数学界和应用数学界十分重视的、前沿的、具有主流兴趣的重要研究课题，有极其重要的理论意义，而且紧密联系应用科学和工程技术实际, 有十分广泛的应用前景。

Magnetohydrodynamics studies the dynamics of quasineutrally ionized fluids under the influence of electromagnetic fields. This project aims to deal with the asymptotic limits and well-posedness to the magnetohydrodynamic equations. These include the low Mach number limit to the compressible isentropic and non-isentropic magnetohydrodynamic equations in a bounded domain, the vanishing viscosity limit to the compressible isentropic and non-isentropic magnetohydrodynamic equations in a bounded domain or half space with Navier boundary condition, the vanishing viscosity limit to the incompressible magnetohydrodynamic equations in a bounded domain with Navier boundary condition, the global existence of the small solutions to the compressible and incompressible magnetohydrodynamic equations with zero magnetic diffusion in a bounded domain, and so on... The above-mentioned research topics are not only very important in international mathematics and applied mathematics community which attach the forefront of mainstream interest, but also extremely important in theoretical significance. There are very broad application prospects in science and engineering.