Reversed Strichartz estimates for wave on non-trapping asymptotically hyperbolic manifolds and applications

Abstract

We provide reversed Strichartz estimates for the shifted wave equations on non-trapping asymptotically hyperbolic manifolds using cluster estimates for spectral projectors proved previously in such generality. As a consequence, we solve a problem left open in Sire et al [Trans. AMS 373(2020):7639-7668] about the endpoint case for global well-posedness of nonlinear wave equations. We also provide estimates in this context for the maximal wave operator.