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

  • Xiaoqi Huang , Xueying Yu , Zehua Zhao EMAIL logo and Jiqiang Zheng
Published/Copyright: June 26, 2024

Abstract

In this paper, we prove Strichartz estimates for many body Schrödinger equations in the periodic setting, specifically on tori 𝕋 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 [J. Bourgain and C. Demeter, The proof of the l 2 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.


Communicated by Christopher D. Sogge


Award Identifier / Grant number: DMS-2306429

Award Identifier / Grant number: 12101046

Award Identifier / Grant number: 12271032

Award Identifier / Grant number: 12271051

Funding statement: Xiaoqi Huang is partially supported by an AMS-Simons travel grant. Xueying Yu is partially supported by NSF DMS-2306429. Zehua Zhao was supported by the NSF grant of China (No. 12101046, 12271032) and the Beijing Institute of Technology Research Fund Program for Young Scholars. Jiqiang Zheng was supported by NSF grant of China (No. 12271051) and Beijing Natural Science Foundation 1222019.

Acknowledgements

The first author and the third author have learned many-body Schrödinger models and related background during their postdoc careers at the University of Maryland. Thus they highly appreciate Professor M. Grillakis, Professor M. Machedon and Dr. J. Chong for related discussions, especially the paper [20] of Hong.

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Received: 2024-02-27
Revised: 2024-05-31
Published Online: 2024-06-26
Published in Print: 2025-02-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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