A moving boundary problem for the Stokes equations involving osmosis:   variational modelling and short-time well-posedness
  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. 
Friedrich Lippoth, Mark A. Peletier, Georg Prokert
math.AP