We prove sharp pointwise kernel estimates and dispersive properties for
the linear wave equation on noncompact Riemannian symmetric spaces
of any
rank with
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.
Keywords
noncompact symmetric space of higher rank, semilinear wave
equation, dispersive property, Strichartz inequality,
global well-posedness
