A Strichartz estimate for de Sitter space

Abstract

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.

9 pages; v3: final version, corrected MSC classes

References in corpus (1)

• The wave equation on asymptotically de Sitter-like spaces

Cited by in corpus (5)

• Global well-posedness of quasilinear wave equations on asymptotically de Sitter spaces
• Global results for linear waves on expanding Kerr and Schwarzschild de Sitter cosmologies
• The Cauchy problem for the Klein-Gordon equation under the quartic potential in the de Sitter spacetime
• On the numerical experiments of the Cauchy problem for semi-linear Klein-Gordon equations in the de Sitter spacetime
• Weak dispersion for the Dirac equation on asymptotically flat and warped products spaces