On the Navier-Stokes equations with slip boundary conditions in 2-D pipe

I will talk about the steady Navier-Stokes equations in a two dimensional channel with slip boundary conditions. Under some restrictions on the shape of the domain and the friction I show existence of solutions with no bounds on largeness of the flux of the flow and the norm of the external force. The crucial point in the proof is the maximum principle for a reformulation of the problem. This technique gives a new type of estimates in the Hölder space for the solutions with the infinite Dirichlet integral.