  We derive two systems of boundary-domain integral equations (BDIEs)
equivalent to the Dirichlet problem for the compressible Stokes system using
the potential method with an explicit parametrix (Levi function). The BDIEs are
given in terms of surface and volume hydrodynamic potentials. We study the
mapping properties of these integral potential operators and used them to prove
existence and uniqueness of solution of the two systems of BDIEs obtained
taking into account the non-trivial kernels of the single layer and
hypersingular hydrodynamic surface potentials.
