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

Abstract

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