  In this paper, we investigate the incompressible steady Navier-Stokes system
with no-slip boundary condition in a two-dimensional channel. Given any flux,
the existence of solutions is proved as long as the width of cross-section of
the channel grows more slowly than the linear growth. Furthermore, if the flux
is suitably small, the solution is unique even when the width of the channel is
unbounded. Finally, based on the estimate of Dirichlet norm on the truncated
domain, one could obtain the pointwise decay rate of the solution for arbitrary
flux.
