Global stability of the viscous non-resistive MHD Rayleigh–Taylor problem in a 3D infinite slab

We investigate the global (in time) stability of the Rayleigh–Taylor problem for the incompressible viscous and non-resistive MHD fluids under the effect of a uniform non-horizontal magnetic field. The fluids are confined within a 3D infinite slab domain and separated by a free interface. Previous research by Wang has established nonlinear stability for the case without surface tension under the sharp stability condition |B̄3|>Mc in [Wang, Arch. Ration. Mech. Anal. 231, 1675–1743 (2019)]. In this paper, we present a new mathematical approach to prove the existence of unique strong solutions along with algebraic time-decay for the MHD Rayleigh–Taylor problem with proper initial data under the condition |B̄3|>Mc. The proof is carried out within the framework of lower-order normal regularity, which requires no nonlinear compatibility conditions on the initial data. Moreover, both cases with and without surface tension are considered.