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

Abstract

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-Pausader \cite{IPRT3} (Comm. Math. Phys. 312 (2012), no. 3, 781-831).

arXiv comment27 pages. Comments are welcome!

References in corpus (6)

• Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrodinger equation in the radial case
• Global well-posedness and scattering for the defocusing, $L^2$-critical, nonlinear Schr{ö}dinger equation when $d=2$
• Global well-posedness of the energy critical Nonlinear Schrödinger equation with small initial data in H^1(T^3)
• Global well-posedness of the energy-critical defocusing NLS on $\mathbb{R}\times {\mathbb{T}}^3$
• Strichartz estimates for partially periodic solutions to Schrödinger equations in 4d and applications
• The energy-critical defocusing NLS on T^3

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