On Strichartz estimate for many body Schrödinger equation in the waveguide setting

2023/01/31 by Zehua Zhao, Zhao, Zehua · 1 citation
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2301.13429

openalex publication_date 2023/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this short paper, we prove Strichartz estimates for N-body Schrödinger equations in the waveguide manifold setting (i.e. on semiperiodic spaces ℝ^m× \mathbbTⁿ where m≥ 3), provided that interaction potentials are small enough (depending on the number of the particles and the universal constants, not on the initial data). The proof combines both the ideas of Tzvetkov-Visciglia \citeTV1 and Hong \citehong2017strichartz. As an immediate application, the scattering asymptotics for this model is also obtained. This result extends Hong \citehong2017strichartz to the waveguide case.

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• Nonlinear Schrödinger equation with Ornstein-Uhlenbeck operator

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