A moving boundary problem for the Stokes equations involving osmosis: Variational modelling and short-time well-posedness

Abstract

Within the framework of variational modelling we derive a one-phase moving boundary problem describing the motion of a semipermeable membrane enclosing a viscous liquid, driven by osmotic pressure and surface tension of the membrane. For this problem we prove the existence of classical solutions for a short-time. © 2015 Cambridge University Press.