Separation of the two-dimensional steady MHD boundary layer

In this paper, we study the separation of the two-dimensional steady MHD boundary layer. When the outer flow satisfies appropriate conditions, we find that there exists a separation point on the boundary. Moreover, the singularity of the solution and the separation point occur simultaneously. Our result shows that the magnetic field has a certain positive effect on preventing the occurrence of separation. This gives a rigorous mathematical verification to previous study (Buckmaster, 1969) on the MHD boundary layer separation.