Strichartz estimates for orthonormal systems on compact manifolds: the non-sharp region

TL;DR

This paper develops new Strichartz estimates for orthonormal systems on compact manifolds, expanding the known results to a broader non-sharp exponent region for various wave and Schrödinger equations.

Contribution

It combines recent sharp-line results with Lieb-Sobolev inequalities and localization techniques to extend Strichartz estimates to non-sharp admissible exponents on compact manifolds.

Findings

Extended Strichartz estimates to non-sharp exponent regions

Unified approach covering wave, Klein-Gordon, and fractional Schrödinger equations

Built on recent advances in Lieb-Sobolev inequalities and localization methods

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}.