Global regularity for the nonlinear wave equation with slightly supercritical power

Abstract

We consider the defocusing nonlinear wave equation $\square u=|u{|}^{p-1}u$ 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 $p=5+\hat{I}´$ where $\hat{I}´\in (0,\hat{I}{´}_0(M_0))$.