Stationary Boundary Value Problems for Compressible Navier-Stokes equations ⋆ P.I. Plotnikov Lavryentyev Institute of Hydrodynamics, Siberian Division of Russian Academy of Sciences, Lavryentyev pr. 15, Novosibirsk 630090, Russia J. Sokolowski * Institut Elie Cartan, Laboratoire de Math´ ematiques, Universit´ e Henri Poincar´ e Nancy 1, B.P. 239, 54506 Vandoeuvre l´ es Nancy Cedex, France Abstract We give the over review of available results on the well-posednes of basic boundary value problem for equations of viscous compressible fluids. ⋆ This paper was prepared in the fall of 2006 during a visit of Pavel I. Plotnikov to the Institute Elie Cartan of the University Henri Poincar´ e Nancy 1. * Corresponding author. Email addresses: plotnikov@hydro.nsc.ru (P.I. Plotnikov), Jan.Sokolowski@iecn.u-nancy.fr (J. Sokolowski). Preprint submitted to Elsevier 22 June 2007