Global well-posedness and scattering for the defocusing cubic Schr\"odinger equation on waveguide $\mathbb{R}^2$ $\times$ $\mathbb{T}^2$

Zehua Zhao

Global well-posedness and scattering for the defocusing cubic Schr\"odinger equation on waveguide $\mathbb{R}^2$ $\times$ $\mathbb{T}^2$

Analysis of PDEs 2019-11-04 v2

Authors: Zehua Zhao

Abstract

We consider the problem of large data scattering for the defocusing cubic nonlinear Schr\"odinger equation on $\mathbb{R}^2$ $\times$ $\mathbb{T}^2$ . This equation is critical both at the level of energy and mass. The key ingredients contain a global-in-time Stricharz estimate, resonant system approximation and profile decomposition. Assuming the large data scattering for the 2d cubic resonant system, we can prove the large data scattering for this problem.

Keywords

global well-posedness scattering defocusing cubic schrödinger equation waveguide strichartz estimate resonant system profile decomposition

Cite

@article{arxiv.1710.09702,
  title  = {Global well-posedness and scattering for the defocusing cubic Schr\"odinger equation on waveguide $\mathbb{R}^2$ $\times$ $\mathbb{T}^2$},
  author = {Zehua Zhao},
  journal= {arXiv preprint arXiv:1710.09702},
  year   = {2019}
}

Comments

40 pages. The author used a compact template which may be better with no big changes. It will appear in Journal of Hyperbolic Differential Equations. arXiv admin note: substantial text overlap with arXiv:1205.6132, arXiv:1101.4527 by other authors

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