Well-posedness of the 3D MHD boundary layer equations in an analytic space

The objective of this paper is to investigate the local well-posedness of analytic solutions to the three-dimensional (3D) magnetohydrodynamic (MHD) boundary layer equations without structural assumptions. Specifically, the general initial data are required to be real-analytic in the tangential variables $(x,y)$ and satisfy Sobolev regularity in the normal variable $z$. We first adopt a variable transformation involving $\varphi (z)$ to homogenize the boundary conditions and eliminate resulting high-order terms. Additionally, we employ delicate energy estimates combined with Gauss weight functions to control linearly growth terms.