  In this paper, we investigate the Leray problem for steady Navier-Stokes
system under full slip boundary conditions in a two dimensional channel with
straight outlets. The existence of solutions with arbitrary flux in a general
channel with slip boundary conditions is established, which tend to the shear
flows at far fields. Furthermore, if the flux is suitably small, the solutions
are proved to be unique. One of the crucial ingredients is to construct an
appropriate flux carrier and to show a Hardy type inequality for flows with
full slip boundary conditions.
