Global endpoint Strichartz estimates for Schr\"odinger equations on the cylinder $\mathbb{R}\times\mathbb{T}$

TL;DR

This paper establishes a precise, global-in-time Strichartz estimate for the Schrödinger equation on the cylindrical domain combining real line and torus, advancing understanding of dispersive PDEs on mixed geometries.

Contribution

It provides the first sharp, global-in-time Strichartz estimate for Schrödinger equations on the cylinder timesa0a0, a significant step in dispersive PDE analysis on non-compact manifolds.

Findings

Proved a sharp, global-in-time Strichartz estimate for Schrödinger on timesa0a0.

Extended dispersive PDE techniques to cylindrical geometries.

Enhanced understanding of Schrödinger dynamics on mixed manifolds.

Abstract

We prove a sharp, global-in-time Strichartz estimate for the Schr\"odinger equation on the cylinder $\mathbb{R}\times\mathbb{T}$.