Global regularity for the nonlinear wave equation with slightly supercritical power

TL;DR

This paper proves global well-posedness for the defocusing nonlinear wave equation with slightly supercritical power in three dimensions, extending known results to powers just above the critical threshold.

Contribution

It establishes global regularity for the nonlinear wave equation with powers slightly above the critical exponent, a significant extension of previous supercritical results.

Findings

Global well-posedness for p=5+δ with small δ

Bounded initial data leads to global solutions

Extension of supercritical regularity results

Abstract

We consider the defocusing nonlinear wave equation $\Box u = \lvert u \rvert^{p-1} u$ in $\mathbb{R}^3 \times[0,\infty)$. We prove that for any initial datum with a scaling-subcritical norm bounded by $M_0$ the equation is globally well-posed for $p=5+\delta$ where $\delta \in (0,\delta_0(M_0))$.