Title 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 2
SJR Quartile 2
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
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