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

TL;DR

This paper derives the precise decay rates of small spherically symmetric solutions to nonlinear wave equations with potential, highlighting the interplay between linear and nonlinear effects in late-time behavior.

Contribution

It provides exact asymptotic decay rates for solutions, advancing understanding of tail phenomena in nonlinear wave equations under spherical symmetry.

Findings

Exact late-time decay rates derived

Linear and nonlinear effects both influence tails

Results applicable to small spherically symmetric solutions

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.