Overdamped Dynamics of a Falling Inextensible Network: Existence of Solutions

TL;DR

This paper investigates the overdamped motion equations of an inextensible triod with fixed ends and a free junction, proving the global existence of solutions using PDE analysis and geometric interpretation.

Contribution

It establishes the first proof of global solutions for the PDE system modeling the inextensible triod's overdamped dynamics, incorporating complex boundary conditions.

Findings

Proved global existence of generalized solutions.

Formulated the problem as a gradient flow in Otto-Wasserstein space.

Connected the PDE model to geometric measure theory.

Abstract

We study the equations of overdamped motion of an inextensible triod with three fixed ends and a free junction under the action of gravity. The problem can be expressed as a system of PDE that involves unknown Lagrange multipliers and non-standard boundary conditions related to the freely moving junction. It can also be formally interpreted as a gradient flow of the potential energy on a certain submanifold of the Otto-Wasserstein space of probability measures. We prove global existence of generalized solutions to this problem.