Prandtl-type boundary layer expansions of the steady Boussinesq-MHD equations

We study the two-dimensional steady Boussinesq-MHD (BMHD) system defined in the domain [0,L]×R+ and obtain the validity of Prandtl-type boundary layer expansions for this system, where the boundary moves with the tangential velocity field, the horizontal magnetic field is nondegenerate, and the temperature field satisfies nonhomogeneous Dirichlet boundary conditions. This work extends the results of Bian and Si [arXiv:2405.09726 (2024)] and Ding, Lin, and Xie [SIAM J. Math. Anal. 53, 4997–5059 (2021)] by considering the presence of the temperature field.