Pointwise decay for semilinear wave equations on Kerr spacetimes

Abstract

In this article we prove optimal pointwise bounds for solutions to the semilinear wave equation with integer powers $p\ge 3$ on Kerr backgrounds with small angular momentum and small initial data.

arXiv comment19 pages, acknowledgments and minor mistakes corrected

References in corpus (13)

• The black hole stability problem for linear scalar perturbations
• A new physical-space approach to decay for the wave equation with applications to black hole spacetimes
• Uniform Decay of Local Energy and the Semi-Linear Wave Equation on Schwarzchild Space
• Strichartz estimates on Schwarzschild black hole backgrounds
• The Strauss conjecture on Kerr black hole backgrounds
• Late-time asymptotics for the wave equation on extremal Reissner-Nordström backgrounds
• A sharp version of Price's law for wave decay on asymptotically flat spacetimes
• A Vector Field Method for Radiating Black Hole Spacetimes
• Quantitative decay rates for dispersive solutions to the Einstein-scalar field system in spherical symmetry
• Pointwise decay for the wave equation on nonstationary spacetimes
• Linear and nonlinear tails I: general results and perturbation theory
• Global Stability of the Nontrivial Solutions to the Wave Map Problem from Kerr $|a|\ll M$ to the Hyperbolic Plane under Axisymmetric Perturbations Preserving Angular Momentum
• Global pointwise decay estimates for defocusing radial nonlinear wave equations

Cited by in corpus (2)

• The weak null condition on Kerr backgrounds
• Sharp decay for Teukolsky equation in Kerr spacetimes