Global well-posedness and scattering for defocusing, cubic NLS in $\mathbb{R}^3$

Qingtang Su

Global well-posedness and scattering for defocusing, cubic NLS in $\mathbb{R}^3$

Analysis of PDEs 2012-02-14 v3

Authors: Qingtang Su

Abstract

We prove global well-posedness and scattering for the defocusing, cubic NLS on $\mathbb{R}^3$ with initial data in $H^s(\mathbb{R}^3)$ for $s>49/74$ . The proof combines the ideas of resonance decomposition in \cite{CKSTT4} and linear-nonlinear decomposition in \cite{ben1}\cite{roy} together with the idea of large time iteration.

Keywords

defocusing cubic NLS global well-posedness scattering resonance decomposition linear-nonlinear decomposition

Cite

@article{arxiv.1111.4021,
  title  = {Global well-posedness and scattering for defocusing, cubic NLS in $\mathbb{R}^3$},
  author = {Qingtang Su},
  journal= {arXiv preprint arXiv:1111.4021},
  year   = {2012}
}

Comments

25 pages, to appear in Math. Research Letter

Related papers

View all related →