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arXiv · 2009.01116

Global Well-posedness for the focusing cubic NLS on the product space $\mathbb{R} \times \mathbb{T}^3$

Xueying Yu·Haitian Yue·Zehua Zhao
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Abstract

In this paper, we prove the global well-posedness for the focusing, cubic nonlinear Schr\"odinger 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-Pausader \cite{IPRT3} (Comm. Math. Phys. 312 (2012), no. 3, 781-831).

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Xueying Yu, Haitian Yue, Zehua Zhao. 2020-09-02. Global Well-posedness for the focusing cubic NLS on the product space $\mathbb{R} \times \mathbb{T}^3$. https://doi.org/10.1137/20m1364953

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