Well-posedness of the three-dimensional NLS equation with sphere-concentrated nonlinearity

被引：0

作者：

Finco, Domenico ^{[1
]}

Tentarelli, Lorenzo ^{[2
]}

Teta, Alessandro ^{[3
]}

机构：

[1] Univ Telematica Int Uninettuno, Fac Ingn, Corso Vittorio Emanuele 2, I-00186 Rome, Italy

[2] Politecn Torino, Dipartimento Sci Matemat GL Lagrange, Corso Duca Abruzzi 24, I-10129 Turin, Italy

[3] Univ Roma La Sapienza, Dipartimento Matemat G Castelnuovo, Piazzale Aldo Moro 5, I-00185 Rome, Italy

来源：

NONLINEARITY | 2024年 / 37卷 / 01期

关键词：

NLS equation; concentrated nonlinearity; unit sphere; well-posedness; spherical harmonics; EXACTLY SOLVABLE MODELS; SCHRODINGER-EQUATION; DIMENSION; 3; BLOW-UP; CAUCHY-PROBLEM; INSTABILITY; IONIZATION; SCATTERING; STATES;

D O I：

10.1088/1361-6544/ad0aac

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页数：48

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