Uniform decay of local energy and the semi-linear wave equation on Schwarzschild space

DOI10.1007/s00220-006-0101-6zbMath1123.58018arXivmath/0510315OpenAlexW1988707400MaRDI QIDQ996028

Publication date: 11 September 2007

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0510315

Mathematics Subject Classification ID

Methods of quantum field theory in general relativity and gravitational theory (83C47) Hyperbolic equations on manifolds (58J45)

Related Items (62)

Mathematical general relativity: A sampler ⋮ Decay for solutions of the wave equation on Kerr exterior spacetimes. III: The full subextremalcase \(|a| < M\). ⋮ A large data theory for nonlinear wave on the Schwarzschild background ⋮ On the global stability of the wave-map equation in Kerr spaces with small angular momentum ⋮ Logarithmic local energy decay for scalar waves on a general class of asymptotically flat spacetimes ⋮ The \(r^{p}\)-weighted energy method of Dafermos and Rodnianski in general asymptotically flat spacetimes and applications ⋮ Superradiant instabilities for short-range non-negative potentials on Kerr spacetimes and applications ⋮ Multi-center vector field methods for wave equations ⋮ The null condition and global existence for nonlinear wave equations on slowly rotating Kerr spacetimes ⋮ Slow decay of waves in gravitational solitons ⋮ Normally hyperbolic trapping on asymptotically stationary spacetimes ⋮ A proof of Price's Law on Schwarzschild black hole manifolds for all angular momenta ⋮ A proof of Friedman's ergosphere instability for scalar waves ⋮ Decay estimates for the massless Vlasov equation on Schwarzschild spacetimes ⋮ Hidden symmetries and decay for the wave equation on the Kerr spacetime ⋮ Stability of Schwarzschild-AdS for the spherically symmetric Einstein-Klein-Gordon system ⋮ Price's law for spin fields on a Schwarzschild background ⋮ Decay of Maxwell fields on Reissner-Nordström-de Sitter black holes ⋮ Global stability for charged scalar fields in an asymptotically flat metric in harmonic gauge ⋮ On the massive wave equation on slowly rotating Kerr-AdS spacetimes ⋮ Improved decay for solutions to the linear wave equation on a Schwarzschild black hole ⋮ A space-time integral estimate for a large data semi-linear wave equation on the Schwarzschild manifold ⋮ Sharp decay for Teukolsky equation in Kerr spacetimes ⋮ Asymptotic behavior of massless Dirac waves in Schwarzschild geometry ⋮ Mathematical aspects of general relativity. Abstracts from the workshop held August 29 -- September 4, 2021 (hybrid meeting) ⋮ Nonlinear scalar perturbations of extremal Reissner-Nordström spacetimes ⋮ Quasi-normal modes and exponential energy decay for the Kerr-de Sitter black hole ⋮ Price's law on nonstationary space-times ⋮ Blow-up and lifespan estimate to a nonlinear wave equation in Schwarzschild spacetime ⋮ A proof of the uniform boundedness of solutions to the wave equation on slowly rotating Kerr backgrounds ⋮ Asymptotic distribution of quasi-normal modes for Kerr-de Sitter black holes ⋮ Resolvent estimates for normally hyperbolic trapped sets ⋮ Stability and instability of extreme Reissner-Nordström black hole spacetimes for linear scalar perturbations. I ⋮ Linear stability of Schwarzschild spacetime: decay of metric coefficients ⋮ A local energy estimate for wave equations on metrics asymptotically close to Kerr ⋮ Global existence for quasilinear wave equations close to Schwarzschild ⋮ Decay and non-decay of the local energy for the wave equation on the De Sitter-Schwarzschild metric ⋮ Price’s Law on Black Hole Space-Times ⋮ Decay of axisymmetric solutions of the wave equation on extreme Kerr backgrounds ⋮ Pointwise decay for the Maxwell field on black hole space-times ⋮ Strichartz estimates on Schwarzschild black hole backgrounds ⋮ Boundedness and decay for the Teukolsky equation on Kerr spacetimes. I: The case \(|a|\ll M\) ⋮ Strong cosmic censorship in spherical symmetry for two-ended asymptotically flat initial data II: the exterior of the Black Hole region ⋮ Lifespan estimate for semilinear wave equation in Schwarzschild spacetime ⋮ DECAY OF THE MAXWELL FIELD ON THE SCHWARZSCHILD MANIFOLD ⋮ The Strauss conjecture on Kerr black hole backgrounds ⋮ Phase space analysis on some black hole manifolds ⋮ Quantitative mode stability for the wave equation on the Kerr spacetime ⋮ Effective limiting absorption principles, and applications ⋮ Morawetz estimate for linearized gravity in Schwarzschild ⋮ Radiation fields on Schwarzschild spacetime ⋮ A vector field method for radiating black hole spacetimes ⋮ The red‐shift effect and radiation decay on black hole spacetimes ⋮ Nonlinear stability for the Maxwell-Born-Infeld system on a Schwarzschild background ⋮ Pointwise decay for semilinear wave equations on Kerr spacetimes ⋮ Localized energy estimates for wave equations on high-dimensional Schwarzschild space-times ⋮ Almost Price's law in Schwarzschild and decay estimates in Kerr for Maxwell field ⋮ Stability and instability of Schwarzschild-AdS for the nonlinear Einstein-Klein-Gordon system ⋮ Nonlinear radiation gauge for near Kerr spacetimes ⋮ Localized Energy Estimates for Wave Equations on (1+4)-dimensional Myers--Perry Space-times ⋮ Asymptotics of linear waves and resonances with applications to black holes ⋮ The stable trapping phenomenon for black strings and black rings and its obstructions on the decay of linear waves

Cites Work

This page was built for publication: Uniform decay of local energy and the semi-linear wave equation on Schwarzschild space