The Dirichlet problem for the Stokes system and the integral equations method

0346697 - MÚ 2011 RIV BG eng J - Journal Article
Medková, Dagmar - Varnhorn, W.
The Dirichlet problem for the Stokes system and the integral equations method.
International Journal of Pure and Applied Mathematics. Roč. 62, č. 1 (2010), s. 49-55. ISSN 1311-8080
R&D Projects: GA AV ČR IAA100190804
Institutional research plan: CEZ:AV0Z10190503
Keywords : Stokes system * layer potential * integral equation * crack
Subject RIV: BA - General Mathematics
http://www.ijpam.eu/contents/2010-62-1/6/index.html

A boundary value problem for the Stokes system is studied in a cracked domain in the Euclidean space, where the Dirichlet condition is specified on the boundary of the domain. The jump of the velocity and the jump of the stress tensor in the normal direction are prescribed on the crack. We construct a solution of this problem in the form of appropriate potentials and determine the unknown source densities via integral equations' systems on the boundary of the domain. The solution is given explicitly in the form of a series. As a consequence, a maximum modulus estimate for the Stokes system is proved.
Permanent Link: http://hdl.handle.net/11104/0187649