On a Mixed Stokes Problem with Variable Viscosity in the 2D Exterior Domain

The boundary-domain integral equations for the mixed boundary value problem for a compressible Stokes system of partial differential equations with variable viscosity in the two-dimensional unbounded domain are considered. An appropriate parametrix is used to reduce this problem to some direct segregated boundary-domain integral equations (BDIEs). The equivalence of the original BVP and the obtained BDIEs are analysed in weighted Sobolev spaces.