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As a continuation of \cite{LXY}, the paper aims to justify the high Reynoldsnumbers limit for the MHD system with Prandtl boundary layer expansion whenno-slip boundary condition is imposed on velocity field and perfect conductingboundary condition on magnetic field. Under the assumption that the viscosityand resistivity coefficients are of the same order and the initial tangentialmagnetic field on the boundary is not degenerate, we justify the validity ofthe Prandtl boundary layer expansion and give a $L^\infty$ estimate on theerror by multi-scale analysis.

Justification of Prandtl Ansatz for MHD boundary layer