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

## TL;DR

This paper establishes global-in-time Strichartz estimates for the Schrödinger equation on manifolds combining Euclidean space and tori, extending previous results and providing sharper bounds.

## Contribution

It generalizes and improves existing global space-time estimates for Schrödinger equations on semiperiodic manifolds of the form R^n x T^d.

## Key findings

- Proves new global-in-time Strichartz estimates for R^n x T^d.
- Extends previous results from R x T^2 to higher dimensions.
- Provides sharper bounds for solutions on semiperiodic manifolds.

## 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.