Endpoint Strichartz estimates for magnetic wave equations on two dimensional hyperbolic spaces

Abstract

In this paper, we prove that the Kato smoothing effects for magnetic half wave operators can yield the endpoint Strichartz estimates for linear wave equations with magnetic potentials on the two dimensional hyperbolic spaces. As a corollary, we obtain the endpoint Strichartz estimates in the case of small potentials. This result serves as a cornerstone for the author's work [27] and collaborative work [29] in the study of asymptotic stability of harmonic maps for wave maps from $ \mathbb R\times \mathbb H^2$ to $ \mathbb H^2$.