Interfaces and Free Boundaries

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Volume 18, Issue 2, 2016, pp. 161–179
DOI: 10.4171/IFB/361

Published online: 2016-09-13

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

Friedrich Lippoth[1] and Georg Prokert[2]

(1) Leibniz Universit├Ąt Hannover, Germany
(2) TU Eindhoven, Netherlands

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 $L_p$-regularity.

Lippoth Friedrich, Prokert Georg: Stability of equilibria of a two-phase Stokes-osmosis problem. Interfaces Free Bound. 18 (2016), 161-179. doi: 10.4171/IFB/361