Boundary-Domain Integral Equations equivalent to an exterior mixed BVP for the variable-viscosity compressible Stokes PDEs

Two direct systems of Boundary-Domain Integral Equations, BDIEs, associated with a mixed boundary value problem for the stationary compressible Stokes system variable viscosity coefficient in an exterior domain $ \mathbb{R}^3 are derived. This is done by employing surface and volume potentials based on appropriate parametrix (Levi function) third Green identities velocity pressure. Mapping properties weighted Sobolev spaces analysed. Finally, equivalence between BDIE BVP shown isomorphism operators defined proved.