On inhibition of the Rayleigh–Taylor instability by a horizontal magnetic field in ideal MHD fluids with velocity damping.

It is still open whether the inhibition phenomenon of the Rayleigh–Taylor (RT) instability by a horizontal magnetic field can be mathematically verified for a non-resistive magnetohydrodynamic (MHD) fluid in a two-dimensional (2D) horizontal slab domain, since it was roughly verified in the linearized case by Wang in [43]. In this paper, we show that this inhibition phenomenon can be rigorously verified in the (nonlinear) inhomogeneous, incompressible, inviscid case with velocity damping. More precisely, we show that there is a critical number m C , such that if the strength | m | of a horizontal magnetic field is bigger than m C , then the small perturbation solution around the magnetic RT equilibrium state is exponentially stable in time. Moreover, we also provide a nonlinear instability result for the case | m | ∈ (0 , m C). Our instability result reveals that a horizontal magnetic field can not inhibit the RT instability, if it's strength is too small. [ABSTRACT FROM AUTHOR]