Global wellposedness of NLS in $H^1(\mathbb{R}) + H^s(\mathbb{T})$

Friedrich Klaus; Peer Kunstmann

Global wellposedness of NLS in $H^1(\mathbb{R}) + H^s(\mathbb{T})$

Analysis of PDEs 2021-09-24 v1

Authors: Friedrich Klaus , Peer Kunstmann

Abstract

We show global wellposedness for the defocusing cubic nonlinear Schr\"odinger equation (NLS) in $H^1(\mathbb{R}) + H^{3/2+}(\mathbb{T})$ , and for the defocusing NLS with polynomial nonlinearities in $H^1(\mathbb{R}) + H^{5/2+}(\mathbb{T})$ . This complements local results for the cubic NLS and global results for the quadratic NLS in this hybrid setting.

Keywords

nonlinear Schrödinger equation global wellposedness hybrid Sobolev space defocusing NLS cubic NLS

Cite

@article{arxiv.2109.11341,
  title  = {Global wellposedness of NLS in $H^1(\mathbb{R}) + H^s(\mathbb{T})$},
  author = {Friedrich Klaus and Peer Kunstmann},
  journal= {arXiv preprint arXiv:2109.11341},
  year   = {2021}
}

Comments

17 pages

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