Rayleigh-Taylor and Parker instabilities in MHD fluids

Abstract

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 Rayleigh-Taylor 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.