Global well-posedness for the focusing cubic nls on the product space R × T3

Xueying Yu; Haitian Yue; Zehua Zhao

doi:10.1137/20M1364953

Global well-posedness for the focusing cubic nls on the product space R × T³

Xueying Yu
, Haitian Yue
, Zehua Zhao

Research output: Contribution to journal › Article › peer-review

17 Citations (Scopus)

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
Pages (from-to)	2243-2274
Number of pages	32
Journal	SIAM Journal on Mathematical Analysis
Volume	53
Issue number	2
DOIs	https://doi.org/10.1137/20M1364953
Publication status	Published - 2021
Externally published	Yes

Keywords

Global well-posedness
NLS
Profile decomposition
Sobolev embedding
Waveguide manifold

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10.1137/20M1364953

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abstract = "In this paper, we prove the global well-posedness for the focusing, cubic nonlinear Schr{\"o}dinger 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].",

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author = "Xueying Yu and Haitian Yue and Zehua Zhao",

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AU - Yu, Xueying

AU - Yue, Haitian

AU - Zhao, Zehua

PY - 2021

Y1 - 2021

N2 - 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].

AB - 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].

KW - Global well-posedness

KW - NLS

KW - Profile decomposition

KW - Sobolev embedding

KW - Waveguide manifold

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ER -

Global well-posedness for the focusing cubic nls on the product space R × T³

Abstract

Keywords

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