We discuss strong local and global well-posedness for the three-dimensional NLS equation with nonlinearity concentrated on S2 . 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.
Well-posedness of the three-dimensional NLS equation with sphere-concentrated nonlinearity / Finco, D; Tentarelli, L; Teta, A. - In: NONLINEARITY. - ISSN 0951-7715. - 37:1(2024). [10.1088/1361-6544/ad0aac]
Well-posedness of the three-dimensional NLS equation with sphere-concentrated nonlinearity
Finco, D;Tentarelli, L;Teta, A
2024
Abstract
We discuss strong local and global well-posedness for the three-dimensional NLS equation with nonlinearity concentrated on S2 . 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.File | Dimensione | Formato | |
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Finco D Tentarelli L Teta A Well-posedness of the three-dimensional NLS equation with sphere-concentrated nonlinearity 2024.pdf
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https://hdl.handle.net/11583/2984780