A note on Strichartz estimates for the wave equation with orthonormal initial data

TL;DR

This paper surveys known Strichartz estimates for the wave equation with orthonormal initial data, discusses open cases, and presents new results in boundary scenarios, advancing understanding of wave behavior with orthonormal initial conditions.

Contribution

It offers a comprehensive survey of existing results, proposes a conjecture for unresolved cases, and introduces new findings in maximal-in-space boundary cases.

Findings

Survey of known Strichartz estimates for wave equations with orthonormal data

Proposed conjecture for open cases in the theory

New results in maximal-in-space boundary scenarios

Abstract

This note is concerned with Strichartz estimates for the wave equation and orthonormal families of initial data. We provide a survey of the known results and present what seems to be a reasonable conjecture regarding the cases which have been left open. We also provide some new results in the maximal-in-space boundary cases.