Boundary partial regularity for steady flows of electrorheological fluids in 3D bounded domains

In this paper, we establish boundary partial regularity for weak solutions to the equations of stationary motion of electrorheological fluids with homogeneous Dirichlet boundary condition in 3D bounded smooth domains. We show that there exists an open subset of the boundary such that Hausdorff dimension of it's complementary set is less than 2 and moreover the velocity, it's gradient and the pressure are Hölder continuous in a neighborhood of any point of the set.