Wave equation on certain noncompact symmetric spaces

TL;DR

This paper establishes sharp kernel estimates and dispersive properties for the wave equation on noncompact symmetric spaces, leading to Strichartz inequalities and global well-posedness results for semilinear equations with low regularity data.

Contribution

It provides the first sharp kernel estimates and dispersive analysis for wave equations on a broad class of noncompact symmetric spaces with complex structures.

Findings

Sharp pointwise kernel estimates derived.

Dispersive properties established for the wave equation.

Global well-posedness proved for semilinear equations with low regularity data.

Abstract

In this paper, we prove sharp pointwise kernel estimates and dispersive properties for the linear wave equation on noncompact Riemannian symmetric spaces G/K of any rank with G complex. As a consequence, we deduce Strichartz inequalities for a large family of admissible pairs and prove global well-posedness results for the corresponding semilinear equation with low regularity data as on hyperbolic spaces.