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We prove the existence and uniqueness of strong solutions to the steadyisentropic compressible Navier-Stokes equations with inflow boundary conditionsfor density and mixed boundary conditions for the velocity around a shear flow.In particular, the Dirichlet boundary condition on inflow and outflow part ofthe boundary while the full Navier boundary conditions on the wall $\Gamma_{0}$for the velocity filed are considered. For our result, there are norestrictions on the amplitude of friction coefficients $\alpha$, and theappropriately large hypothesis for the viscous coefficients $\mu$ is enough.One of the substantial ingredients of our proof is an elegant transformationinduced by the flow field. With the help of this transformation, we canovercome the difficulties caused by the hyperbolicity of continuity equation,establish the a priori estimates for a linearized system and apply the fixedpoint arguments.

On an inhomogeneous slip-inflow boundary value problems for a steady viscous compressible channel flows