论文标题
三维NLS方程的适应性良好
Well-posedness of the three-dimensional NLS equation with sphere-concentrated nonlinearity
论文作者
论文摘要
我们讨论了三维NLS方程的强大本地和全球适应性，非线性集中在$ \ mathbb {s}^2 $上。确切地说，对于任何$ c^2 $ dower-nlinelearity，局部适应性都可以证明，而在某些增长假设下，用于小型数据或在散落的情况下获得了全球适应性。在文献中广泛研究的点浓缩的NLS模型方面，非线性支持的维度不允许直接扩展已知技术并需要新想法。
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.
