磁流体力学Rayleigh-Taylor与Parker不稳定性

Rayleigh-Taylor and Parker instabilities in MHD fluids

本文主要介绍近几年关于可压缩/不可压缩磁流体力学非线性稳定和不稳定性问题的数学分析结果,其中包括不可压情形的磁Rayleigh-Taylor(RT)不稳定性问题和可压情形的Parker不稳定性(磁浮力不稳定性)问题.特别地,本文从数学上分析了(平衡)磁场对不稳定性增长的影响,刻画了一些因素(如区域的几何形状和边界条件等)如何影响不稳定性的增长.此外,本文也介绍了重力作用下黏弹性流体中Rayleigh-Taylor问题的数学分析结果.

We present a brief survey of recent mathematical results on the stability and instability of magnetohydrodynamic flows in the presence of a gravitational field,which include the incompressible magnetic RayleighTaylor instability,and the Parker instability（i.e.,the magnetic buoyancy instability） in compressible magnetohydrodynamics.In particular,the stabilizing effect of some factors（e.g.,steady magnetic fields,boundary conditions,domains） are analyzed.In addition,the mathematical results on the Rayleigh-Taylor instability problem in viscoelastic flows are discussed.