We discuss strong local and global well--posedness for the three--dimensional NLS equation with nonlinearity concentrated on $\S$. 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, Domenico; Tentarelli, Lorenzo; Teta, Alessandro. - In: NONLINEARITY. - ISSN 0951-7715. - 37:(2023). [10.1088/1361-6544/ad0aac]
Well-posedness of the three-dimensional NLS equation with sphere-concentrated nonlinearity
Alessandro Teta
2023
Abstract
We discuss strong local and global well--posedness for the three--dimensional NLS equation with nonlinearity concentrated on $\S$. 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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