The local structure of the energy landscape in multiphase mean curvature flow: Weak-strong uniqueness and stability of evolutions

We prove that in the absence of topological changes, the notion of BV solutions to planar multiphase mean curvature flow does not allow for a mechanism for (unphysical) non-uniqueness. Our approach is based on the local structure of the energy landscape near a classical evolution by mean curvature....

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Published in:arXiv.org 2020-03
Main Authors: Fischer, Julian, Hensel, Sebastian, Laux, Tim, Simon, Thilo
Format: Article
Language:English
Subjects:
Calibration
Curvature
Flow stability
Gradient flow
Multiphase
Surface energy
Uniqueness
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Hensel, Sebastian
Laux, Tim
Simon, Thilo
description We prove that in the absence of topological changes, the notion of BV solutions to planar multiphase mean curvature flow does not allow for a mechanism for (unphysical) non-uniqueness. Our approach is based on the local structure of the energy landscape near a classical evolution by mean curvature. Mean curvature flow being the gradient flow of the surface energy functional, we develop a gradient-flow analogue of the notion of calibrations. Just like the existence of a calibration guarantees that one has reached a global minimum in the energy landscape, the existence of a "gradient flow calibration" ensures that the route of steepest descent in the energy landscape is unique and stable.
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subjects Calibration
Curvature
Flow stability
Gradient flow
Multiphase
Surface energy
Uniqueness
title The local structure of the energy landscape in multiphase mean curvature flow: Weak-strong uniqueness and stability of evolutions
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