  In this paper, we investigate the incompressible steady Navier-Stokes system
with Navier slip boundary condition in a two-dimensional channel. As long as
the width of cross-section of the channel grows more slowly than the linear
growth, the existence of solutions with arbitrary flux is established.
Furthermore, if the flux is suitably small, the solution is unique even when
the width of the channel is unbounded, and approaches to the shear flows at far
field where the channels tend to be straight at far fields. One of the major
difficulties for the analysis on flows with Navier boundary conditions is that
the tangential velocity may not be zero on the boundary so that we have to
study the behavior of solutions near the boundary carefully. The crucial
ingredients of analysis include the construction of an appropriate flux
carrier, and the detailed analysis for the flow behavior near boundary via
combining a Hardy type inequality for normal component of velocity and the
divergence free property of the velocity.
