Non-decay of the energy for a system of semilinear wave equations

TL;DR

This paper establishes conditions under which the energy of small solutions to a two-component cubic semilinear wave system in two dimensions does not decay over time, based on initial data radiation fields.

Contribution

It provides a new criterion linking initial data radiation fields to the non-decay of energy in semilinear wave systems.

Findings

Energy remains non-decaying for certain initial data configurations.

The criterion applies to small amplitude solutions in two-dimensional space.

Radiation fields are key to understanding long-term energy behavior.

Abstract

We consider the global Cauchy problem for a two-component system of cubic semilinear wave equations in two space dimensions. We give a criterion for large time non-decay of the energy for small amplitude solutions in terms of the radiation fields associated with the initial data.