Existence of weak solutions for two-phase matrix-valued harmonic map flows
Analysis of PDEs
2025-07-03 v2 Differential Geometry
Abstract
We investigate the existence of weak solutions for matrix-valued two-phase harmonic map flows with optimal lifespan, which arises as the limiting system of the matrix-valued Rubinstein-Sternberg-Keller problem studied by ({\em Invent. Math.}, 233(1):1--80, 2023). Our approach employs a modified minimizing movement scheme, discretizing the time domain and constructing approximate solutions by interpolating solutions to the associated functional problem within each small time interval.
Cite
@article{arxiv.2506.16278,
title = {Existence of weak solutions for two-phase matrix-valued harmonic map flows},
author = {Wei Wang and Wei Wang and Zhifei Zhang},
journal= {arXiv preprint arXiv:2506.16278},
year = {2025}
}
Comments
34 pages, all comments are welcome!