**Tomasz Piasecki**

**Afilliation:**Polish Academy of Sciences, Institute of Mathematics

**Title:**Stationary compressible flow with slip - inflow boundary conditions

**Abstract:**I am going to discuss the issue of existence of stationary solutions to the Navier Stokes system describing the flow of a compressible, barotropic fluid in a cylindrical domain. On the boundary we prescribe inhomogeneous slip conditions on the velocity. More precisely, we are interested in strong solutions in a vicinity of given laminar flows, such as a constant flow or a Poiseuille-like profile. The common feature of flows under consideration is that the normal component of the velocity does not vanish on the boundary, hence we have to prescribe the velocity on the inflow part. A main problem to face in the proof is the lack of compactess in the continuity equation. To overcome this diffuculty we can introduce a kind of Lagrangian coordinates. In the new system the continuity equation simplifies enabling us to apply the Banach Fixed Point Theorem.