Stokes system with a solution dependent slip bound: Stability of solutions with respect to domains

• ID: 2726, RIV: 10330629
• ISSN: 0044-2267, ISBN: not specified
• source: ZAMM Zeitschrift für Angewandte Mathematik und Mechanik
• keywords: Stokes problem; slip boundary conditions ; stability of solutions w.r. to domains
• authors: Jaroslav Haslinger, Jan Stebel
• authors from KNM: Haslinger Jaroslav

Abstract

The paper deals with the Stokes system in a planar bounded domain with a friction type boundary condition and a threshold bound which depends on the solution itself. Under appropriate assumptions the existence and uniqueness of the solution is proven and the stability of solutions to a mixed variational formulation of the problem with respect to a class of domains is established. These results can be used to prove the existence of optimal shapes in a class of shape optimization problems governed by the Stokes system with the threshold boundary conditions.