# Numerical simulations for the energy-supercritical nonlinear wave equation

## TL;DR

This paper presents numerical simulations of the energy-supercritical nonlinear wave equation, showing that the critical Sobolev norm remains bounded over time, supporting recent theoretical scattering results.

## Contribution

It provides the first numerical evidence that solutions to the energy-supercritical nonlinear wave equation have bounded Sobolev norms, supporting conjectures about their long-term behavior.

## Key findings

- Critical Sobolev norm remains bounded in simulations
- Supports conditional scattering results for nonlinear wave equations
- Numerical evidence for long-term stability of solutions

## Abstract

We carry out numerical simulations of the defocusing energy-supercritical nonlinear wave equation for a range of spherically-symmetric initial conditions. We demonstrate numerically that the critical Sobolev norm of solutions remains bounded in time. This lends support to conditional scattering results that have been recently established for nonlinear wave equations.