Variational approach to nonlinear gravity-driven instabilities in a MHD setting

We establish a variational framework for nonlinear instabilities in a setting of the ideal magnetohydrodynamic (MHD) equations. We apply a variational method to various kind of smooth steady states which are shown to be nonlinearly unstable for both incompressible and compressible ideal MHD equations. Destabilizing effect of compressibility is justified as well as stabilizing effect of magnetic field lines arising in MHD dynamics, which distinguishes from the Rayleigh-Taylor instability in the absence of magnetic field lines.