Well-posedness of the three-dimensional NLS equation with sphere-concentrated nonlinearity
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866911743645581312 |
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| author | Finco, Domenico Tentarelli, Lorenzo Teta, Alessandro |
| author_facet | Finco, Domenico Tentarelli, Lorenzo Teta, Alessandro |
| contents | We discuss strong local and global well-posedness for the three-dimensional NLS equation with nonlinearity concentrated on $\mathbb{S}^2$. Precisely, local well-posedness is proved for any $C^2$ power-nonlinearity, while global well-posedness is obtained either for small data or in the defocusing case under some growth assumptions. With respect to point-concentrated NLS models, widely studied in the literature, here the dimension of the support of the nonlinearity does not allow a direct extension of the known techniques and calls for new ideas. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_13504 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Well-posedness of the three-dimensional NLS equation with sphere-concentrated nonlinearity Finco, Domenico Tentarelli, Lorenzo Teta, Alessandro Analysis of PDEs Mathematical Physics Functional Analysis 81Q35, 35Q40, 35Q55, 35R06, 33C55, 33C10, 33C45, 44A15, 47A60 We discuss strong local and global well-posedness for the three-dimensional NLS equation with nonlinearity concentrated on $\mathbb{S}^2$. Precisely, local well-posedness is proved for any $C^2$ power-nonlinearity, while global well-posedness is obtained either for small data or in the defocusing case under some growth assumptions. With respect to point-concentrated NLS models, widely studied in the literature, here the dimension of the support of the nonlinearity does not allow a direct extension of the known techniques and calls for new ideas. |
| title | Well-posedness of the three-dimensional NLS equation with sphere-concentrated nonlinearity |
| topic | Analysis of PDEs Mathematical Physics Functional Analysis 81Q35, 35Q40, 35Q55, 35R06, 33C55, 33C10, 33C45, 44A15, 47A60 |
| url | https://arxiv.org/abs/2209.13504 |