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arXiv · 1910.02510

Strichartz estimates and Strauss conjecture on non-trapping asymptotically hyperbolic manifolds

Yannick Sire·Christopher D. Sogge·Chengbo Wang·Junyong Zhang
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Abstract

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}.

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Yannick Sire, Christopher D. Sogge, Chengbo Wang, Junyong Zhang. 2019-10-06. Strichartz estimates and Strauss conjecture on non-trapping asymptotically hyperbolic manifolds. https://arxiv.org/abs/1910.02510

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