On Strichartz estimates for many-body Schrödinger equation in the periodic setting

2023/04/03 by Huang, Xiaoqi, Yu, Xueying, Zhao, Zehua +1
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2304.00882

Abstract

In this paper, we prove Strichartz estimates for many body Schrödinger equations in the periodic setting, specifically on tori \mathbbT^d, where d≥ 3. The results hold for both rational and irrational tori, and for small interacting potentials in a certain sense. Our work is based on the standard Strichartz estimate for Schrödinger operators on periodic domains, as developed in Bourgain-Demeter \citeBD. As a comparison, this result can be regarded as a periodic analogue of Hong \citehong2017strichartz though we do not use the same perturbation method. We also note that the perturbation method fails due to the derivative loss property of the periodic Strichartz estimate.

Related

• Strichartz estimates for the periodic non elliptic Schrodinger equation
• Strichartz estimates for the Schrodinger equation on irrational tori
• Strichartz estimates for Schroedinger equations with periodic potential in 1D
• On Strichartz estimate for many body Schrödinger equation in the waveguide setting
• Refinements of Strichartz estimates on tori and applications