Semilinear wave equations on the Schwarzschild manifold I: Local decay estimates

Abstract

The semilinear wave equation on the (outer) Schwarzschild manifold is studied. We prove local decay estimates for general (non-radial) data, deriving a-priori Morawetz type estimates.

arXiv commentAMS-LaTeX, 16 pages. There is an errata to this paper at gr-qc/0608073

References in corpus (1)

• Decay Rates and Probability Estimates for Massive Dirac Particles in the Kerr-Newman Black Hole Geometry

Cited by in corpus (40)

• Stability and Instability of Extreme Reissner-Nordström Black Hole Spacetimes for Linear Scalar Perturbations I
• Stability and Instability of Extreme Reissner-Nordström Black Hole Spacetimes for Linear Scalar Perturbations II
• A proof of the uniform boundedness of solutions to the wave equation on slowly rotating Kerr backgrounds
• Uniform Decay of Local Energy and the Semi-Linear Wave Equation on Schwarzchild Space
• Strichartz estimates on Schwarzschild black hole backgrounds
• A proof of Price's Law on Schwarzschild black hole manifolds for all angular momenta
• Phase Space Analysis on some Black Hole Manifolds
• The Strauss conjecture on Kerr black hole backgrounds
• The wave equation on the Schwarzschild metric II: Local decay for the spin 2 Regge Wheeler equation
• A proof of Friedman's ergosphere instability for scalar waves
• Pointwise decay for the Maxwell field on black hole space-times
• Errata for ``Global existence and scattering for the nonlinear Schrodinger equation on Schwarzschild manifolds'', ``Semilinear wave equations on the Schwarzschild manifold I: Local Decay Estimates'', and ``The wave equation on the Schwarzschild metric II: Local Decay for the spin 2 Regge Wheeler equation''
• Long time existence for semilinear wave equations on asymptotically flat space-times
• A sharp version of Price's law for wave decay on asymptotically flat spacetimes
• Scalar waves on a naked-singularity background
• The Strauss conjecture on asymptotically flat space-times
• Sharp decay estimates for massless Dirac fields on a Schwarzschild background
• Improved decay rates with small regularity loss for the wave equation about a Schwarzschild black hole
• The Wave Equation on Extreme Reissner-Nordström Black Hole Spacetimes: Stability and Instability Results
• Price's law for spin fields on a Schwarzschild background
• The $r^p$-weighted energy method of Dafermos and Rodnianski in general asymptotically flat spacetimes and applications
• Boundedness and decay for the Teukolsky equation of spin $\pm 1$ on Reissner-Nordström spacetime: the $\ell =1$ spherical mode
• Nonlinear radiation gauge for near Kerr spacetimes
• Asymptotic Behavior of Massless Dirac Waves in Schwarzschild geometry
• Pointwise decay for the wave equation on nonstationary spacetimes
• Almost Price's law in Schwarzschild and decay estimates in Kerr for Maxwell field
• The red-shift effect and radiation decay on black hole spacetimes
• Abstract theory of decay estimates: perturbed Hamiltonians
• Local decay of waves on asymptotically flat stationary space-times
• Price's Law on Nonstationary Spacetimes
• Localized energy estimates for wave equations on high dimensional Schwarzschild space-times
• Near Sharp Strichartz estimates with loss in the presence of degenerate hyperbolic trapping
• Localized energy estimates on Myers-Perry space-times
• Nonlinear Wave Equations With Null Condition On Extremal Reissner-Nordström Spacetimes I: Spherical Symmetry
• A note on the wave equation on black hole spacetimes with small non-decaying first order terms
• Multi-center Vector Field Methods for Wave Equations
• Sharp decay for Teukolsky equation in Kerr spacetimes
• Global existence for a coupled wave system related to the Strauss conjecture
• Small-amplitude nonlinear waves on a black hole background
• Differential Equations of Quantum Mechanics