Global Analysis of Quasilinear Wave Equations on Asymptotically Kerr-de Sitter Spaces

@article{Hintz2016GlobalAO,
  title={Global Analysis of Quasilinear Wave Equations on Asymptotically Kerr-de Sitter Spaces},
  author={P. Hintz and A. Vasy},
  journal={International Mathematics Research Notices},
  year={2016},
  volume={2016},
  pages={5355-5426}
}
  • P. Hintz, A. Vasy
  • Published 2016
  • Mathematics
  • International Mathematics Research Notices
We consider quasilinear wave equations on manifolds for which infinity has a structure generalizing that of Kerr-de Sitter space; in particular the trapped geodesics form a normally hyperbolic invariant manifold. We prove the global existence and decay, to constants for the actual wave equation, of solutions. The key new ingredient compared to earlier work by the authors in the semilinear case [33] and by the first author in the non-trapping quasilinear case [30] is the use of the Nash-Moser… Expand
GLOBAL WELL-POSEDNESS OF QUASILINEAR WAVE EQUATIONS ON ASYMPTOTICALLY DE SITTER SPACES
Global existence for quasilinear wave equations close to Schwarzschild
Quasilinear waves and trapping: Kerr-de Sitter space
Resonances for asymptotically hyperbolic manifolds: Vasy's method revisited
The global non-linear stability of the Kerr-de Sitter family of black holes
Resonance expansions for tensor-valued waves on asymptotically Kerr-de Sitter spaces
Asymptotics for the wave equation on differential forms on Kerr-de Sitter space
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References

SHOWING 1-10 OF 54 REFERENCES
Semilinear wave equations on asymptotically de Sitter, Kerr–de Sitter and Minkowski spacetimes
The Null Condition and Global Existence for Nonlinear Wave Equations on Slowly Rotating Kerr Spacetimes
  • J. Luk
  • Physics, Mathematics
  • 2010
Local decay of waves on asymptotically flat stationary space-times
Microlocal analysis of asymptotically hyperbolic and Kerr-de Sitter spaces (with an appendix by Semyon Dyatlov)
Phase Space Analysis on some Black Hole Manifolds
...
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3
4
5
...