Global analysis of quasilinear wave equations on asymptotically Kerr-de Sitter spaces
arXiv:1404.1348 · doi:10.1093/imrn/rnv311
Abstract
We extend the semilinear framework developed by the two authors and the non-trapping quasilinear theory developed by the first author to solve quasilinear wave equations with normally hyperbolic trapping. The most well-known example that fits into our general framework is wave-type equations on Kerr-de Sitter space. The key advance is an adaptation of the Nash-Moser iteration to our framework.
55 pages, 5 figures. v2 is the published version, with an extended introduction, additional figures, and many minor corrections throughout
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Cited by in corpus (10)
- Analysis of linear waves near the Cauchy horizon of cosmological black holes
- Non-linear stability of the Kerr-Newman-de Sitter family of charged black holes
- Stability of Minkowski space and polyhomogeneity of the metric
- A sharp version of Price's law for wave decay on asymptotically flat spacetimes
- Normally hyperbolic trapping on asymptotically stationary spacetimes
- A local energy estimate for wave equations on metrics asymptotically close to Kerr
- Strichartz estimate and nonlinear Klein-Gordon on non-trapping scattering space
- On turbulence for spacetimes with stable trapping
- Uniqueness of Kerr-Newman-de Sitter black holes with small angular momenta
- Overdamped quasibound states inside a Schwarzschild black hole