In this paper we study the nonlinear stability of Ekman-Hartmann-type boundary layers in a rotating magnetohydrodynamics flow in a half-space and between two planes. We prove rigorously that if the Reynolds number defined on boundary-layer characteristics is smaller than a critical value, the boundary layer is nonlinearly stable. It is shown that the normal component of the magnetic field increases the critical Reynolds number for instability.
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Desjardins et al. (1999) studied this question.