  We study the small-time global approximate controllability for incompressible
magnetohydrodynamic (MHD) flows in smoothly bounded two- or three-dimensional
domains. The controls act on arbitrary nonempty open portions of each connected
boundary component, while linearly coupled Navier slip-with-friction conditions
are imposed along the uncontrolled parts of the boundary. Some choices for the
friction coefficients give rise to interacting velocity and magnetic field
boundary layers. We obtain sufficient dissipation properties of these layers by
a detailed analysis of the corresponding asymptotic expansions. For certain
friction coefficients, or if the obtained controls are not compatible with the
induction equation, an additional pressure-like term appears. We show that such
a term does not exist for problems defined in planar simply-connected domains
and various choices of Navier slip-with-friction boundary conditions.
