Existence of weak solutions and regular solutions to the incompressible Schrödinger flow
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911578091159552 |
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| author | Chen, Bo Wang, Guangwu Wang, Youde |
| author_facet | Chen, Bo Wang, Guangwu Wang, Youde |
| contents | In this paper, we are concerned with the initial-Neumann boundary value problem of the Schrödinger flow for maps from a smooth bounded domain in an Euclidean space into $\mathbb{S}^2$. By adopting a novel method due to B. Chen and Y.D. Wang, we prove the existence of short-time regular solutions to this flow within the framework of Sobolev spaces when the underlying space is a smooth bounded domain in $\mathbb{R}^m$ with $m\leq 3$. Moreover, we also utilize the ``complex structure approximation method" to establish the global existence of weak solutions to the incompressible Schrödinger flow in a smooth bounded domain of $\mathbb{R}^m$ (where $m\geq 1$). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_07696 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Existence of weak solutions and regular solutions to the incompressible Schrödinger flow Chen, Bo Wang, Guangwu Wang, Youde Analysis of PDEs In this paper, we are concerned with the initial-Neumann boundary value problem of the Schrödinger flow for maps from a smooth bounded domain in an Euclidean space into $\mathbb{S}^2$. By adopting a novel method due to B. Chen and Y.D. Wang, we prove the existence of short-time regular solutions to this flow within the framework of Sobolev spaces when the underlying space is a smooth bounded domain in $\mathbb{R}^m$ with $m\leq 3$. Moreover, we also utilize the ``complex structure approximation method" to establish the global existence of weak solutions to the incompressible Schrödinger flow in a smooth bounded domain of $\mathbb{R}^m$ (where $m\geq 1$). |
| title | Existence of weak solutions and regular solutions to the incompressible Schrödinger flow |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2604.07696 |