On the cubic NLS on 3D compact domains

Fabrice Planchon

doi:10.1017/S1474748013000017

On the cubic NLS on 3D compact domains

Analysis of PDEs 2021-08-23 v2

Authors: Fabrice Planchon

View on arXiv ↗ PDF ↗ DOI ↗

Abstract

We prove bilinear estimates for the Schr\"odinger equation on 3D domains, with Dirichlet boundary conditions. On non-trapping domains, they match the $\mathbb{R}^3$ case, while on bounded domains they match the generic boundary less manifold case. As an application, we obtain global well-posedness for the defocusing cubic NLS for data in $H^s_0(\Omega)$ , $1<s\leq 3$ , with $\Omega$ any bounded domain with smooth boundary.

Keywords

cubic NLS Schrödinger equation bilinear estimates Dirichlet boundary conditions global well-posedness 3D compact domains non-trapping domains

Cite

@article{arxiv.1210.4362,
  title  = {On the cubic NLS on 3D compact domains},
  author = {Fabrice Planchon},
  journal= {arXiv preprint arXiv:1210.4362},
  year   = {2021}
}

Comments

15 pages, updated references and corrected typos. To appear in Journal of the Institute of Mathematics of Jussieu

Related papers

View all related →