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On the Well-Posedness of Two Boundary-Domain Integral Equation Systems Equivalent to the Dirichlet Problem for the Stokes System with Variable Viscosity

Authors

Dagnaw, M. A. , FRESNEDA PORTILLO, CARLOS

External publication

No

Means

Results Math.

Scope

Article

Nature

Científica

JCR Quartile

✓

SJR Quartile

✗

JCR Impact

2.2

SJR Impact

0.556

Web

https://www.scopus.com/inward/record.uri?eid=2-s2.0-85127268224&doi=10.1007%2fs00025-022-01630-7&partnerID=40&md5=2ef00067028be83eaa10e81788e563f9

Publication date

01/06/2022

ISI

000780372900001

Scopus Id

2-s2.0-85127268224

DOI

10.1007/s00025-022-01630-7

Abstract

We derive two systems of boundary-domain integral equations (BDIEs) equivalent to the Dirichlet problem for the compressible Stokes system using the potential method with an explicit parametrix (Levi function). The BDIEs are given in terms of the surface and volume hydrodynamic potentials. The mapping properties of these integral potential operators are analysed and applied to prove existence and uniqueness of solution of the two systems of BDIEs obtained taking into account the non-trivial kernels of the single layer and hypersingular hydrodynamic surface potentials.

Keywords

35J25; 31B10; 45K05; 45A05; 76N20