The Immersed Inextensible Interface Problem in 2D Stokes Flow

TL;DR

This paper investigates the mathematical modeling, well-posedness, and numerical analysis of an inextensible interface in 2D Stokes flow, providing insights into its dynamics and long-term behavior.

Contribution

It formulates a boundary integral approach for the inextensible interface problem and proves well-posedness and smoothness of solutions, with initial numerical exploration of long-term dynamics.

Findings

Well-posedness in suitable function spaces

Smoothness of solutions for positive times

Numerical insights into long-time behavior

Abstract

We study the dynamics of an inextensible, closed interface subject to bending forces and immersed in a two-dimensional and incompressible Stokes fluid. We formulate the problem as a boundary integral equation in terms of the tangent angle and demonstrate the well-posedness in suitable time-weighted spaces of the resulting nonlinear and nonlocal system. The solution is furthermore shown to be smooth for positive times. Numerical computations are performed to initiate the study of the long-time behavior of the interface.