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

Baskin, Dean

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

Keywords:

conformally invariant Klein-Gordon equation; rescaling argument; semilinear Klein-Gordon equation