Existence of weak solutions for two-phase matrix-valued harmonic map flows
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916822095233024 |
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| author | Wang, Wei Wang, Wei Zhang, Zhifei |
| author_facet | Wang, Wei Wang, Wei Zhang, Zhifei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_16278 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence of weak solutions for two-phase matrix-valued harmonic map flows Wang, Wei Wang, Wei Zhang, Zhifei Analysis of PDEs Differential Geometry 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. |
| title | Existence of weak solutions for two-phase matrix-valued harmonic map flows |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2506.16278 |