  We investigate a steady flow of compressible fluid with inflow boundary
condition on the density and slip boundary conditions on the velocity in a
square domain in $\mathbf{R^2}$. We show existence of a strong solution
$(v,\rho) \in W^2_p(Q) \times W^1_p(Q)$ that is a small perturbation of a
constant flow $(\bar v \equiv [1,0],\bar \rho \equiv 1)$. We also show that
this solution is unique in a class of small perturbations of the constant flow
$(\bar v,\bar \rho)$. In order show the existence of the solution we adapt the
techniques know from the theory of weak solutions. We apply the method of
elliptic regularization and a fixed point argument.
