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

Document Type

Article

Publication Date

5-1-2025

Abstract

In this paper, we prove Strichartz estimates for many body Schrödinger equations in the periodic setting, specifically on tori Td, 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 [J. Bourgain and C. Demeter, The proof of the l2 decoupling conjecture, Ann. of Math. (2) 182 2015, 1, 351-389]. As a comparison, this result can be regarded as a periodic analogue of [Y. Hong, Strichartz estimates for N-body Schrödinger operators with small potential interactions, Discrete Contin. Dyn. Syst. 37 2017, 10, 5355-5365] 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.

Publication Source (Journal or Book title)

Forum Mathematicum

First Page

997

Last Page

1008

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