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This is a Observational study (also classified as: Numerical Study).

On Diffusion and Transport Acting on Parameterized Moving Closed Curves in Space

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Local existence and uniqueness of classical Hölder smooth solutions are proven for the governing nonlinear parabolic equations.
A direct Lagrangian approach leads to a system of degenerate parabolic equations describing the flow of 3D curves.
Numerical examples illustrate the evolution of closed curves in 3D space along with scalar quantities.
The study addresses flow behaviors of curves with zero torsion in both rotating and parallel planes.

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Analysis reveals local existence of Hölder smooth solutions for evolving closed curves, suggesting numerical methods can model complex curve flows.

Beneš et al. (2025) studied this question.

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Analysis reveals local existence of Hölder smooth solutions for evolving closed curves, suggesting numerical methods can model complex curve flows.