Linear and nonlinear tails II: exact decay rates in spherical symmetry

Abstract

We derive the exact late-time asymptotics for small spherically symmetric solutions of nonlinear wave equations with a potential. The dominant tail is shown to result from the competition between linear and nonlinear effects.

17 pages, 3 figures, 2 tables

References in corpus (5)

• On asymptotic stability of the Skyrmion
• Late-time tails of a Yang-Mills field on Minkowski and Schwarzschild backgrounds
• Anomalously small wave tails in higher dimensions
• Weighted-$L^{\infty }$ and pointwise space-time decay estimates for wave equations with potentials and initial data of low regularity
• Simple proof of a useful pointwise estimate for the wave equation

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• Global pointwise decay estimates for defocusing radial nonlinear wave equations
• Numerical computation of electromagnetically sourced nonlinear tails
• Asymptotics from scaling for nonlinear wave equations
• Late-time attractor for the cubic nonlinear wave equation
• A hyperboloidal method for numerical simulations of multidimensional nonlinear wave equations: nonlinear tails