Global well-posedness of the free-surface incompressible ideal MHD equations with velocity damping
摘要
This paper concerns the free-surface problem of incompressible ideal MHD fluids with velocity damping in a two-dimensional (2D) horizontally periodic slab domain impressed by a uniform horizontal magnetic field. We prove that the problem is globally well-posed for the small initial data and the solution decays exponentially in time to the equilibrium, where both the Taylor sign condition and the surface tension are not required in this paper due to the stabilizing effect of horizontal magnetic field.