Scattering for defocusing energy subcritical nonlinear wave equations

Abstract

We consider the Cauchy problem for the defocusing power-type nonlinear wave equation in $\left(1+3\right)$-dimensions for energy subcritical powers $p$ in the superconformal range $3<p<5$. We prove that any solution is global-in-time and scatters to free waves in both time directions as long as its critical Sobolev norm stays bounded on the maximal interval of existence.