Self-consistent three-dimensional steady state solutions of the MHD equations with field-aligned incompressible flow

We present self-consistent steady state solutions of the three-dimensional MHD equations including held-aligned incompressible flow. The solutions are calculated by a transformation method which allows the construction of ste ady state MHD solutions with subalfvenic flow from known solutions of stati c MHD and of steady state MHD solutions with superalfvenic flow from known solutions of steady state hydrodynamics. For the first time this transforma tion method is used to calculate self-consistent three-dimensional solution s of the steady state MHD equations with flow. We discuss possible applicat ions of particular solutions to flow phenomena in the solar atmosphere such as the Evershed flow in sunspots and flows in coronal arcades.