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

Xueying Yu, Haitian Yue, Zehua Zhao

Research output: Contribution to journalArticlepeer-review

16 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 languageEnglish
Pages (from-to)2243-2274
Number of pages32
JournalSIAM Journal on Mathematical Analysis
Volume53
Issue number2
DOIs
Publication statusPublished - 2021
Externally publishedYes

Keywords

  • Global well-posedness
  • NLS
  • Profile decomposition
  • Sobolev embedding
  • Waveguide manifold

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