Summary: The Navier-Stokes system for a steady-state barotropic nonlinear compressible viscous flow, with an inflow boundary condition, is studied on a polygon \(D\). A unique existence for the solution of the system is established. It is shown that the lowest-order corner singularity of the nonlinear system is the same as that of the Laplacian in suitable \(L^q\) spaces. Let \(\omega\) be the interior angle of a vertex \(P\) of \(D\). If \(\alpha := \frac{\pi}{\omega}<2\) and \(q>\frac{2}{2-\alpha}\), then the velocity u is split into singular and regular parts near the vertex \(P\) . If \(\alpha < 2\) and \(2<q<\frac{2}{2-\alpha}\) or if \(\alpha > 2\) and \(2 < q < \infty\), it is shown that \(\mathbf u \in ( H^{2,q} (D))^2\).