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 Ω⊂ℝ3$$ \Omega \subset {\mathrm{\mathbb{R}}}^3 $$ with the no‐slip boundary condition for the velocity u$$ \mathbf{u} $$ and inhomogeneous generalized impermeability boundary conditions for the magnetic field b$$ \mathbf{b} $$. The main results concern an appropriate definition of the weak solution (u,b)$$ \left(\mathbf{u},\mathbf{b}\right) $$, its existence, continuous dependence on the data when the data tend to zero, and uniqueness in a "small" neighborhood of the zero solution (0,0)$$ \left(\mathbf{0},\mathbf{0}\right) $$. [ABSTRACT FROM AUTHOR]