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arXiv · 2201.05547

Overdamped Dynamics of a Falling Inextensible Network: Existence of Solutions

Ayk Telciyan·Dmitry Vorotnikov
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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.

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Ayk Telciyan, Dmitry Vorotnikov. 2022-01-14. Overdamped Dynamics of a Falling Inextensible Network: Existence of Solutions. https://arxiv.org/abs/2201.05547

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