关于可压缩MHD方程组的若干研究进展

Some Recent Results on Compressible MHD Equations

主要介绍近年来关于可压缩磁流体力学(MHD)方程组的若干研究进展,主要包括:一维可压缩MHD方程组古典解的存在唯一性和剪切粘性极限,三维可压缩MHD方程组的整体解存在性和不可压极限,以及三维可压缩MHD方程组整体强解的爆破准则.

In this paper,we recall some recent mathematical results on the compressible magnehydrodynamics（MHD）,including the global exisntece and uniqeness of classical solution and the vanishing shear viscosity limit to the 1-D MHD equations,the global existence of solution and the incomressible limit to the 3-D MHD equations,and the blow-up criteria of strong solution for the 3-D MHD equations with vacuum states.