  We construct $L_p$-estimates for the inhomogeneous Oseen system studied in a
two dimensional exterior domain $\Omega$ with inhomogeneous slip boundary
conditions. The kernel of the paper is a result for the half space
$\mathbb{R}^2_+$. Analysis of this model system shows us a parabolic character
of the studied problem, resulting as an appearance of the wake region behind
the obstacle. Main tools are given by the Fourier analysis to obtain the
maximal regularity estimates. The results imply the solvability for the
Navier-Stokes system for small velocity at infinity.
