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

Abstrakt

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.

Klíčová slova

• Stokes problem
• slip boundary conditions
• stability of solutions w.r. to domains