Title BOUNDARY-DOMAIN INTEGRAL EQUATIONS EQUIVALENT TO AN EXTERIOR MIXED BVP FOR THE VARIABLE-VISCOSITY COMPRESSIBLE STOKES PDES
Authors Mikhailov, Sergey E. , FRESNEDA PORTILLO, CARLOS
External publication No
Means Commun. Pure Appl. Anal.
Scope Article
Nature Científica
JCR Quartile 2
SJR Quartile 1
Area International
Web https://www.scopus.com/inward/record.uri?eid=2-s2.0-85103798642&doi=10.3934%2fCPAA.2021009&partnerID=40&md5=270a77829d1c82b881a7490d22fff9ff
Publication date 01/03/2021
ISI 000627872700009
Scopus Id 2-s2.0-85103798642
DOI 10.3934/cpaa.2021009
Abstract Two direct systems of Boundary-Domain Integral Equations, BDIEs, associated with a mixed boundary value problem for the stationary compressible Stokes system with variable viscosity coefficient in an exterior domain of R3 are derived. This is done by employing the Stokes surface and volume potentials based on an appropriate parametrix (Levi function) in the third Green identities for the velocity and pressure. Mapping properties of the potentials in weighted Sobolev spaces are analysed. Finally, the equivalence between the BDIE systems and the BVP is shown and the isomorphism of operators defined by the BDIE systems is proved.
Keywords Partial differential equations; Stokes system; compressibility; variable viscosity coefficient; exterior domain; parametrix; Levi function; integral potentials; boundary-domain integral equations; wei
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