流体运动中磁场的稳定作用

Stabilizing effects of magnetic field on fluid motion

介绍本团队近几年在磁流体力学方程组(MHD)的理论研究中关于磁场对流体运动的稳定作用方面的相关工作.主要包括:二维非完全耗散MHD柯西问题的稳定性,粘性无磁扩散MHD Rayleigh-Taylor问题的稳定性,无粘带磁扩散MHD自由界面问题的整体适定性以及理想MHD高维接触间断解的存在性.最后也将提及一些尚未解决的问题.

Some of our recent works on the stabilizing effects of the magnetic field on the fluid motion in the theoretical research of magnetohydrodynamics(MHD)equations are introduced.These stabilizing effects include the stability of the Cauchy problem for the 2D non-fully dissipative MHD,the stability of the Rayleigh-Taylor problem for the viscous non-resistive MHD,the global well-posedness of the free interface problem for the inviscid resistive MHD,and the existence of multi-dimensional contact discontinuities solutions for the ideal MHD.Furthermore,some unsolved problems are mentioned.