Wave maps in dimension $1+1$ with an external forcing
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911839082774528 |
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| author | Brzeźniak, Zdzisław Jendrej, Jacek Rana, Nimit |
| author_facet | Brzeźniak, Zdzisław Jendrej, Jacek Rana, Nimit |
| contents | This paper aims to establish the local and global well-posedness theory in $L^1$, inspired by the approach of Keel and Tao [Internat. Math. Res. Notices, 1998], for the forced wave map equation in the ``external'' formalism. In this context, the target manifold is treated as a submanifold of a Euclidean space. As a corollary, we reprove Zhou's [Math. Z., 1999] uniqueness result, leading to the uniqueness of weak solutions with locally finite energy. Additionally, we achieve the scattering of such solutions through a conformal compactification argument. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_09195 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Wave maps in dimension $1+1$ with an external forcing Brzeźniak, Zdzisław Jendrej, Jacek Rana, Nimit Analysis of PDEs This paper aims to establish the local and global well-posedness theory in $L^1$, inspired by the approach of Keel and Tao [Internat. Math. Res. Notices, 1998], for the forced wave map equation in the ``external'' formalism. In this context, the target manifold is treated as a submanifold of a Euclidean space. As a corollary, we reprove Zhou's [Math. Z., 1999] uniqueness result, leading to the uniqueness of weak solutions with locally finite energy. Additionally, we achieve the scattering of such solutions through a conformal compactification argument. |
| title | Wave maps in dimension $1+1$ with an external forcing |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2404.09195 |