Analysis of Boundary-Domain Integral Equations to the Mixed BVP for a Compressible Stokes System with Variable Viscosity

TL;DR

This paper develops boundary-domain integral equations for a compressible Stokes system with variable viscosity, proving their equivalence to the original boundary value problem and establishing operator invertibility in Sobolev spaces.

Contribution

It introduces two new BDIE systems for the mixed BVP of a compressible Stokes system with variable viscosity and proves their equivalence and operator invertibility.

Findings

BDIE systems are equivalent to the mixed BVP.

Invertibility of associated matrix operators is established.

The approach applies in appropriate Sobolev spaces.

Abstract

The mixed boundary value problem for a compressible Stokes system of partial differential equations in a bounded domain is reduced to two different systems of segregated direct Boundary Integral Equations (BDIEs) expressed in terms of surface and volume parametrix-based potential type operators. Equivalence of the BDIE systems to the mixed BVP and invertibility of the matrix operators associated with the BDIE systems are proved in appropriate Sobolev spaces.