# Scattering for critical wave equations with variable coefficients

**Authors:** Shi-Zhuo Looi, Mihai Tohaneanu  
**arXiv:** [1912.06795](https://arxiv.org/abs/1912.06795)  
**Date:** 2019-12-14  
**Summary page:** https://www.summarizepaper.com/fr/arxiv-id/1912.06795v1/

## Abstract

We prove that solutions to the quintic semilinear wave equation with variable coefficients in $\mathbb R^{1+3}$ scatter to a solution to the corresponding linear wave equation. The coefficients are small and decay as $|x|\to\infty$, but are allowed to be time dependent. The proof uses local energy decay estimates to establish the decay of the $L^6$ norm of the solution as $t\to\infty$.