Abstract
In this paper, we prove the global well-posedness for the focusing, cubic nonlinear Schrödinger equation on the product space R × T3 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].
Original language | English |
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Pages (from-to) | 2243-2274 |
Number of pages | 32 |
Journal | SIAM Journal on Mathematical Analysis |
Volume | 53 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2021 |
Externally published | Yes |
Keywords
- Global well-posedness
- NLS
- Profile decomposition
- Sobolev embedding
- Waveguide manifold