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

TL;DR

This paper formulates a variational model for a moving boundary problem involving the Stokes equations and osmosis, proving short-time existence of classical solutions.

Contribution

It introduces a novel variational approach to model membrane motion driven by osmotic pressure and surface tension, establishing well-posedness.

Findings

Existence of classical solutions for short times

A new variational formulation for osmosis-driven boundary problems

Mathematical proof of 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.