Convergence of the Neumann series in BEM for the Neumann problem of the stokes system

0367466 - MÚ 2012 RIV NL eng J - Journal Article
Medková, Dagmar
Convergence of the Neumann series in BEM for the Neumann problem of the stokes system.
Acta Applicandae Mathematicae. Roč. 116, č. 3 (2011), s. 281-304. ISSN 0167-8019. E-ISSN 1572-9036
R&D Projects: GA AV ČR IAA100190804
Institutional research plan: CEZ:AV0Z10190503
Keywords : stokes system * Neumann problem * integral equation method
Subject RIV: BA - General Mathematics
Impact factor: 0.899, year: 2011
http://www.springerlink.com/content/d73174l507577464/

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.
Permanent Link: http://hdl.handle.net/11104/0202143