On pointwise decay of waves

Abstract

This article serves as an introduction to the linear aspects of the recent submission by Krieger, Miao, and the author, see arXiv:2009.08843. It also surveys some of the results obtained on the decay of linear waves on various backgrounds or in the presence of a potential over the past 15 years. Particular emphasis is placed on the role of 0 energy. The techniques are based on spectral and scattering theory. Note that this is not a systematic review, as this would require a book.

arXiv commentThis article is dedicated to the memory of Jean Bourgain. 5 figures are included. Revised version, to appear in Journal Math. Phys

References in corpus (21)

• Dispersive estimates for Schrodinger operators in dimensions one and three
• A proof of Price's law for the collapse of a self-gravitating scalar field
• Decay of Solutions of the Wave Equation in the Kerr Geometry
• A proof of Price's Law on Schwarzschild black hole manifolds for all angular momenta
• Dispersive estimates for Schroedinger operators in dimension two
• Improved decay for solutions to the linear wave equation on a Schwarzschild black hole
• L^p boundedness of the wave operator for the one dimensional Schroedinger operator
• Phase Space Analysis on some Black Hole Manifolds
• New Estimates for a Time-Dependent Schroedinger Equation
• Schrödinger dispersive estimates for a scaling-critical class of potentials
• Characterisation of the Energy of Gaussian Beams on Lorentzian Manifolds - with Applications to Black Hole Spacetimes
• A counterexample to dispersive estimates for Schrödinger operators in higher dimensions
• An introduction to fractal uncertainty principle
• Dispersive estimates for Schrödinger operators in dimension two with obstructions at zero energy
• A weighted dispersive estimate for Schrödinger operators in dimension two
• A sharp version of Price's law for wave decay on asymptotically flat spacetimes
• Dispersive estimates for Dirac Operators in dimension three with obstructions at threshold energies
• On the $L^p$ boundedness of wave operators for two-dimensional Schrödinger operators with threshold obstructions
• Semiclassical low energy scattering for one-dimensional Schrödinger operators with exponentially decaying potentials
• Decay estimates for the one-dimensional wave equation with an inverse power potential
• A stability theory beyond the co-rotational setting for critical Wave Maps blow up

Cited by in corpus (4)

• Late-time asymptotics for geometric wave equations with inverse-square potentials
• Dispersive estimates for higher order Schrödinger operators with scaling-critical potentials
• The Massless Dirac Equation in Three Dimensions: Dispersive estimates and zero energy obstructions
• Price's law on Minkowski space in the presence of an inverse square potential