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

Abstract

We show global wellposedness for the defocusing cubic nonlinear Schrodinger 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 [6] and global results for the quadratic NLS [8] in this hybrid setting.