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.
2024
File in questo prodotto:
File Dimensione Formato  
Finco D Tentarelli L Teta A Well-posedness of the three-dimensional NLS equation with sphere-concentrated nonlinearity 2024.pdf

accesso aperto

Tipologia: 2a Post-print versione editoriale / Version of Record
Licenza: Creative commons
Dimensione 557.97 kB
Formato Adobe PDF
557.97 kB Adobe PDF Visualizza/Apri
Finco_Tentarelli_Teta_revisedversion.pdf

accesso aperto

Tipologia: 2. Post-print / Author's Accepted Manuscript
Licenza: Creative commons
Dimensione 531.03 kB
Formato Adobe PDF
531.03 kB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2984780