Strichartz Estimates on Asymptotically De Sitter Spaces
نویسنده
چکیده
In this article we prove a family of local (in time) weighted Strichartz estimates with derivative losses for the KleinGordon equation on asymptotically de Sitter spaces and provide a heuristic argument for the non-existence of a global dispersive estimate on these spaces. The weights in the estimates depend on the mass parameter and disappear in the “large mass” regime. We also provide an application of these estimates to establish smalldata global existence for a class of semilinear equations on these spaces.
منابع مشابه
A Strichartz estimate for de Sitter space
We demonstrate a family of Strichartz estimates for the conformally invariant KleinGordon equation on a class of asymptotically de Sitter spaces with C2 metrics by using well-known local Strichartz estimates and a rescaling argument. This class of metrics includes de Sitter space. We also give an application of the estimates to a semilinear Klein-Gordon equation on these spaces.
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