On steady solutions to the MHD equations with inhomogeneous generalized impermeability boundary conditions for the magnetic field

The paper deals with the steady MHD equations for a viscous incompressible fluid in a bounded and generally multiply connected domain (Formula presented.) with the no-slip boundary condition for the velocity (Formula presented.) and inhomogeneous generalized impermeability boundary conditions for the magnetic field (Formula presented.). The main results concern an appropriate definition of the weak solution (Formula presented.), its existence, continuous dependence on the data when the data tend to zero, and uniqueness in a “small” neighborhood of the zero solution (Formula presented.).