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arXiv · 2506.16278

Existence of weak solutions for two-phase matrix-valued harmonic map flows

Wei Wang·Zhifei Zhang
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Abstract

We study the existence of weak solutions to a two-phase matrix-valued harmonic map flow with lifespan determined by that of the prescribed interface. This system arises as the limiting equation for the matrix-valued Keller--Rubinstein--Sternberg problem studied in (Invent. Math., 233(1):1--80, 2023). Our construction is based on a modified minimizing movement scheme. Precisely, we discretize time and build approximate solutions by interpolating minimizers of the associated variational problem on each time step.

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Wei Wang, Zhifei Zhang. 2025-06-19. Existence of weak solutions for two-phase matrix-valued harmonic map flows. https://doi.org/10.1016/j.jfa.2026.111623

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