A Strichartz estimate for de Sitter space.(English)Zbl 1227.35101

Hassell, Andrew (ed.) et al., The AMSI-ANU workshop on spectral theory and harmonic analysis. Proceedings of the workshop, Canberra, Australia, July 13–17, 2009. Canberra: Australian National University, Centre for Mathematics and its Applications (ISBN 978-0-7315-5208-5). Proceedings of the Centre for Mathematics and its Applications, Australian National University 44, 97-104 (2010).
Summary: We demonstrate a family of Strichartz estimates for the conformally invariant Klein-Gordon equation on a class of asymptotically de Sitter spaces with $$C^2$$ 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.
For the entire collection see [Zbl 1218.47003].

MSC:

 35B45 A priori estimates in context of PDEs 35Q75 PDEs in connection with relativity and gravitational theory 58J45 Hyperbolic equations on manifolds 35L71 Second-order semilinear hyperbolic equations
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