We prove global-in-time Strichartz estimates for the shifted wave equations on non-trapping asymptotically hyperbolic manifolds. The key tools are the spectral measure estimates from \cite{ CH2} and arguments borrowed from \cite{ HZ, Zhang}. As an application, we prove the small data global existence for any power $p\in(1, 1+\frac{ 4}{ n-1})$ for the shifted wave equation in this setting, involving nonlinearities of the form $\pm|u|^p$ or $\pm|u|^{ p-1}u$, which answers partially an open question raised in \cite{ SSW}.
Categories: math.AP