#### Vol. 13, No. 7, 2020

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Scattering for defocusing energy subcritical nonlinear wave equations

### Benjamin Dodson, Andrew Lawrie, Dana Mendelson and Jason Murphy

Vol. 13 (2020), No. 7, 1995–2090
##### 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. 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.

##### Keywords
nonlinear waves, scattering
Primary: 35L71