Periodic Schrödinger map flow on Kähler manifolds
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866929243696398336 |
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| author | Wang, Sheng Zhou, Yi |
| author_facet | Wang, Sheng Zhou, Yi |
| contents | Wei-Yue Ding \cite{Ding 2002} proposeed a proposition about Schrödinger map flow in 2002 International Congress of Mathematicians in Beijing, which is called Wei-Yue Ding conjecture by Rodnianski-Rubinstein-Staffilani \cite{Rodnianski 2009}. They proved \cite{Rodnianski 2009} that Schrödinger map flow for maps from the real line into Kähler manifolds and for maps from the circle into Riemann surfaces is globally well-posed which is the first significant advance in this conjecture by translating the Schrödinger map flow into nonlinear Schrödinger-type equations or (systems) and partially solved this conjecture. In this article, we will derive a new div-curl type lemma and combined it with energy and ``momentum" balance law to get some space-time estimates. Based on this, we prove the Schrödinger map flow for maps from the circle into Kähler manifolds is globally regular. So far, the Wei-Yue Ding's conjecture has been completely solved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_09969 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Periodic Schrödinger map flow on Kähler manifolds Wang, Sheng Zhou, Yi Analysis of PDEs Wei-Yue Ding \cite{Ding 2002} proposeed a proposition about Schrödinger map flow in 2002 International Congress of Mathematicians in Beijing, which is called Wei-Yue Ding conjecture by Rodnianski-Rubinstein-Staffilani \cite{Rodnianski 2009}. They proved \cite{Rodnianski 2009} that Schrödinger map flow for maps from the real line into Kähler manifolds and for maps from the circle into Riemann surfaces is globally well-posed which is the first significant advance in this conjecture by translating the Schrödinger map flow into nonlinear Schrödinger-type equations or (systems) and partially solved this conjecture. In this article, we will derive a new div-curl type lemma and combined it with energy and ``momentum" balance law to get some space-time estimates. Based on this, we prove the Schrödinger map flow for maps from the circle into Kähler manifolds is globally regular. So far, the Wei-Yue Ding's conjecture has been completely solved. |
| title | Periodic Schrödinger map flow on Kähler manifolds |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2302.09969 |