Strichartz estimates on asymptotically de Sitter spaces

Details Strichartz estimates on asymptotically de Sitter spaces Strichartz estimates on asymptotically de Sitter spaces

2010-11-21

arxiv.org/abs/1011.4696v4

Mathematics

Analysis of PDEs

36 pages; minor changes made in response to referee report

Scientific paper

In this article we prove a family of local (in time) weighted Strichartz estimates with derivative losses for the Klein-Gordon 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 small-data global existence for a class of semilinear equations on these spaces.

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