  We investigate the existence and the zero viscosity limit of steady
compressible shear flow with Navier-slip boundary condition in the absence of
any external force in a two-dimension domain $\Omega=(0,L)\times(0,2)$. More
precisely, under the assumption that the Mach number $\eta<\va^{\f12+}$ and
$L\ll1$, we prove the existence of smooth solutions to steady compressible
Naiver-Stokes equations near plane Poiseuille-Couette flow as well as the
convergence of the solutions obtained above to the solutions of steady
incompressible Euler equations when the viscous $\va$ tends to zero.
