Some United Boundary-Domain Integral and Integro-Differential Equations to the Dirichlet BVP for a Compressible Stokes System with Variable Viscosity

Abstract

The Dirichlet boundary value problem (BVP) for a compressible Stokes
system of partial differential equations (PDEs) with variable viscosity is considered in a
bounded three dimensional domain. Using an appropriate parametrix (Levi function),
the problem is reduced to the united boundary-domain integro-differential equation
(BDIDE) or to a domain integral equation supplemented by the original boundary
condition, thus constituting a boundary-domain integro-differential problem (BDIDP).
Solvability, solution uniqueness and equivalence of the BDIDE/BDIDP to the original
BVP as well as invertibility of the associated operators are analysed in appropriate
Sobolev (Bessel potential) spaces.