Abstract: This article studies the initial-boundary value problem for a three dimensional magnetic-curvature-driven Rayleigh-Taylor model. We first obtain the global existence of weak solutions for the full model equation by employing the Galerkin's approximation method. Secondly, for a slightly simplified model, we show the existence and uniqueness of global strong solutions via the Banach's fixed point theorem and vanishing viscosity method.

Key words: Magnetic-curvature-driven Rayleigh-Taylor model, weak solutions, strong solutions, Banach fixed point theorem, vanishing viscosity method