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arXiv · 2509.06125

Curvature Flow of Networks with Triple Junction Drag

Yuchuan Yang·Selim Esedoglu
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Abstract

We consider a PDE system that describes curvature motion of networks with a dynamic boundary condition known as triple junction drag. This model arises in the study of grain boundary evolution in polycrystalline materials. In this system, the surface tension coefficients depend on the crystallographic orientations of the grains, which are allowed to rotate. We prove existence and uniqueness of solutions to this system in the parabolic H\"{o}lder class $C^{2+\alpha,1+\alpha/2}$. Moreover, we extend our existence result to accommodate a wider class of initial networks by relaxing the compatibility conditions on the angles and curvatures at the triple junction. As an important by-product of our result, we demonstrate the possibility of a new type of topological change during the evolution of the network. We also revisit the question of stability of stationary networks and how it is affected by the choice of surface tensions.

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Yuchuan Yang, Selim Esedoglu. 2025-09-07. Curvature Flow of Networks with Triple Junction Drag. https://arxiv.org/abs/2509.06125

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