Wave equation on certain noncompact symmetric spaces

Hong-Wei Zhang (1, 2)

1 IDP - Institut Denis Poisson
2 UGENT - Universiteit Gent = Ghent University

In this paper, we prove sharp pointwise kernel estimates and dis-persive 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.

Mots clés: Symmetric space; Wave equation; Dispersive estimate

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]

Hong-Wei Zhang. Wave equation on certain noncompact symmetric spaces. Pure and Applied Analysis, 2021. ⟨hal-02905019v3⟩