Strichartz estimates for orthonormal systems on compact manifolds: the non-sharp region
Abstract
We establish new Strichartz estimates for orthonormal systems on compact Riemannian manifolds in the non-sharp admissible region of exponents, covering wave, Klein-Gordon, and fractional Schr\"odinger equations. Our approach combines the result of Wang-Zhang-Zhang \cite{wang2025strichartz} on the sharp admissible line with a Lieb-Sobolev inequality derived from a recent Cwikel estimate due to Sukochev-Yang-Zanin \cite{sukochev2025singular}, along with an alternative globalization method based on localized weak Lorentz estimates. Our results extend the Euclidean results of Bez-Hong-Lee-Nakamura-Sawano \cite{bez2019strichartz} and Bez-Lee-Nakamura \cite{bez2021strichartz}, as well as the classical single-function estimates on manifolds due to Kapitanski \cite{kapitanski1989some}, Burq-G\'erard-Tzvetkov \cite{MR2058384}, and Dinh \cite{dinh2016strichartz}.
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Cite
@article{arxiv.2605.09336,
title = {Strichartz estimates for orthonormal systems on compact manifolds: the non-sharp region},
author = {Hongzhou Ji and Liping Xu and An Zhang},
journal= {arXiv preprint arXiv:2605.09336},
year = {2026}
}
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31 pages