Simple proof of a useful pointwise estimate for the wave equation

Abstract

We give a simple proof of a pointwise decay estimate in 3+1 dimensions stated in two versions, making advantage of a particular simplicity of inverting the spherically symmetric part of the wave operator and of the comparison theorem. We briefly explain the role of this estimate in proving decay estimates for nonlinear wave equations or wave equations with potential terms.

7 pages; some minor errors corrected; numerical values of the bounds added

References in corpus (1)

• Weighted-$L^{\infty }$ and pointwise space-time decay estimates for wave equations with potentials and initial data of low regularity

Cited by in corpus (4)

• Linear and nonlinear tails II: exact decay rates in spherical symmetry
• Pointwise decay for the wave equation on nonstationary spacetimes
• Large data pointwise decay for defocusing semilinear wave equations
• Comment on "Late-time tails of a self-gravitating massless scalar field revisited" by Bizon et al: The leading order asymptotics