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Convergence of the Neumann series in BEM for the Neumann problem of the stokes system
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SYSNO ASEP 0367466 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Convergence of the Neumann series in BEM for the Neumann problem of the stokes system Author(s) Medková, Dagmar (MU-W) RID, SAI, ORCID Source Title Acta Applicandae Mathematicae - ISSN 0167-8019
Roč. 116, č. 3 (2011), s. 281-304Number of pages 24 s. Language eng - English Country NL - Netherlands Keywords stokes system ; Neumann problem ; integral equation method Subject RIV BA - General Mathematics R&D Projects IAA100190804 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR) CEZ AV0Z10190503 - MU-W (2005-2011) UT WOS 000300084300004 EID SCOPUS 84855316570 DOI 10.1007/s10440-011-9643-5 Annotation A weak solution of the Neumann problem for the Stokes system in Sobolev space is studied in a bounded Lipschitz domain with connected boundary. A solution is looked for in the form of a hydrodynamical single layer potential. It leads to an integral equation on the boundary of the domain. Necessary and sufficient conditions for the solvability of the problem are given. Moreover, it is shown that we can obtain a solution of this integral equation using the successive approximation method. Then the consequences for the direct boundary integral equation method are treated. A solution of the Neumann problem for the Stokes system is the sum of the hydrodynamical single layer potential corresponding to the boundary condition and the hydrodynamical double layer potential corresponding to the trace of the velocity part of the solution. Using boundary behavior of potentials we get an integral equation on the boundary of the domain where the trace of the velocity part of the solution is unknown. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2012
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