Vol. 14, No. 4, 2021

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On global-in-time Strichartz estimates for the semiperiodic Schrödinger equation

Alex Barron

Vol. 14 (2021), No. 4, 1125–1152
Abstract

We prove global-in-time Strichartz-type estimates for the Schrödinger equation on manifolds of the form n × 𝕋d , where 𝕋d is a d-dimensional torus. Our results generalize and improve a global space-time estimate for the Schrödinger equation on × 𝕋2 due to Z. Hani and B. Pausader. As a consequence we prove global existence and scattering in H12 for small initial data for the quintic NLS on × 𝕋 and the cubic NLS on 2 × 𝕋.

Keywords
Strichartz estimates on product space, Schrödinger equation on waveguide, decoupling
Mathematical Subject Classification 2010
Primary: 35Q55
Secondary: 42B37
Milestones
Received: 22 February 2019
Revised: 5 September 2019
Accepted: 2 December 2019
Published: 6 July 2021
Authors
Alex Barron
Department of Mathematics
University of Illinois Urbana-Champaign
Urbana, IL
United States