Wave and Klein-Gordon equations on certain locally symmetric spaces

TL;DR

This paper investigates the dispersive behavior of Klein-Gordon and wave equations on specific locally symmetric spaces, establishing Strichartz estimates and global well-posedness for semilinear cases with low regularity data.

Contribution

It extends dispersive analysis and well-posedness results to a class of locally symmetric spaces, generalizing known results from real hyperbolic spaces.

Findings

Established Strichartz estimates for Klein-Gordon and wave equations on these spaces.

Proved global well-posedness for semilinear equations with low regularity data.

Demonstrated dispersive properties extend beyond real hyperbolic spaces.

Abstract

This paper is devoted to study the dispersive properties of the linear Klein-Gordon and wave equations on a class of locally symmetric spaces. As a consequence, we obtain the Strichartz estimate and prove global well-posedness results for the corresponding semilinear equation with low regularity data as on real hyperbolic spaces.