A remark on almost sure global well-posedness of the energy-critical defocusing nonlinear wave equations in the periodic setting

TL;DR

This paper proves that the energy-critical defocusing nonlinear wave equations on periodic domains are almost surely globally well-posed for random initial data below the energy space in dimensions 3, 4, and 5.

Contribution

It establishes almost sure global well-posedness for the energy-critical defocusing nonlinear wave equations with sub-energy initial data on periodic domains.

Findings

Almost sure global well-posedness in dimensions 3, 4, and 5.

Handles initial data below the energy space.

Extends previous results to periodic settings.

Abstract

In this note, we prove almost sure global well-posedness of the energy-critical defocusing nonlinear wave equation on $\mathbb{T}^d$, $d = 3, 4,$ and $5$, with random initial data below the energy space.