Strichartz estimates for the Klein-Gordon equation in a conical singular space

TL;DR

This paper establishes global-in-time Strichartz estimates for the Klein-Gordon equation with inverse-square potentials on conical singular spaces, advancing understanding of wave behavior in singular geometric settings.

Contribution

It provides the first proof of global Strichartz estimates for Klein-Gordon equations with inverse-square potentials on conical spaces.

Findings

Proves global-in-time Strichartz estimates in conical singular spaces.

Analyzes Klein-Gordon equations with inverse-square potentials.

Extends harmonic analysis techniques to singular geometric settings.

Abstract

Consider a conical singular space $X=C(Y)=(0,\infty)_r\times Y$ with the metric $g=\mathrm{d}r^2+r^2h$, where the cross section $Y$ is a compact $(n-1)$-dimensional closed Riemannian manifold $(Y,h)$. We study the Klein-Gordon equations with inverse-square potentials in the space $X$, proving in particular global-in-time Strichartz estimates in this setting.