On Global-in-Time Strichartz Estimates for the Semiperiodic Schrödinger Equation

Abstract

We prove global-in-time Strichartz-type estimates for the Schrödinger 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 Schrödinger equation on $\mathbb{R}\times {\mathbb{T}}^2$ due to Z. Hani and B. Pausader.

Added a new section with nonlinear applications. Some additional minor changes/corrections

References in corpus (1)

• On scattering for the defocusing quintic nonlinear Schrödinger equation on the two-dimensional cylinder

Cited by in corpus (5)

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• Well-posedness for energy-critical nonlinear Schrödinger equation on waveguide manifold
• Hyperbolic nonlinear Schrödinger equations on $\mathbb{R}\times \mathbb{T}$
• Bilinear estimate for Schrödinger equation on $\mathbb{R}\times \mathbb{T}$
• Global endpoint Strichartz estimates for Schrödinger equations on the cylinder $\mathbb{R}\times \mathbb{T}$