Stability of equilibria of a two-phase Stokes-osmosis problem

Within the framework of variational modelling we derive a two-phase moving boundary problem that describes the motion of a semipermeable membrane separating two viscous liquids in a fixed container. The model includes the effects of osmotic pressure and surface tension of the membrane. For this problem we prove that the manifold of steady states is locally exponentially attractive. Keywords: variational modelling, two-phase Stokes equations, osmosis, moving boundary problem, maximal Lp-regularit