On Global-in-Time Strichartz Estimates for the Semiperiodic Schr\"{o}dinger Equation

Abstract

We prove global-in-time Strichartz-type estimates for the Schr\"{o}dinger equation on manifolds of the form $\mathbb{R}^{n}\times \mathbb{T}^{d}$, where $\mathbb{T}^{d}$ is a $d$-dimensional torus. Our results generalize and improve a global space-time estimate for the Schr\"{o}dinger equation on $\mathbb{R} \times \mathbb{T}^{2}$ due to Z. Hani and B. Pausader.