Global solvability of 2D MHD boundary layer equations in analytic function spaces

In this paper we are concerned with the global well-posedness of solutions to magnetohydrodynamics (MHD) boundary layer equations in analytic function spaces. When initial data is a small perturbation around selected profile, and such profile governed by an one dimensional heat equation source term, establish time existence uniqueness two (2D) MHD equations. It noted that far-field state velocity not required be initially, but decays zero as tends infinity suitable decay rates. The whole analysis divided into parts: states small, reformulate original problem extracting background which equation, then prove long-time solutions, lower bound lifespan given term parameter perturbation; After establishing existence, combining properties it shown both solution obtained first part indeed satisfy some smallness requirements when goes solutions. Then can show after moment.