SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 2243-2274, January 2021.
In this paper, we prove the global well-posedness for the focusing, cubic nonlinear Schrödinger equation on the product space $\mathbb{R} \times \mathbb{T}^3$ with initial data below the threshold that arises from the the ground state in the Euclidean setting. The defocusing analogue was discussed and proved in Ionescu and Pausader [Comm. Math. Phys., 312 (2012), pp. 781--831].

中文翻译：

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产品空间上立方NLS的全局适定性$ \ mathbb {R} \ times \ mathbb {T} ^ 3 $

SIAM数学分析杂志，第53卷，第2期，第2243-2274页，2021
年1月。在本文中，我们证明了积空间$ \ mathbb {R} \上的聚焦立方非线性Schrödinger方程的全局适定性。乘以\ mathbb {T} ^ 3 $，其初始数据低于在欧几里得设置中的基态引起的阈值。Ionescu和Pausader讨论并证明了散焦类似物。数学。物理学报，312（2012），第781--831页]。