# A Note on Decay Rates of the Local Energy for Wave Equations with Lipschitz Wavespeeds

## TL;DR

This paper improves the understanding of how quickly the local energy decays over time for wave equations with Lipschitz continuous wave speeds, extending previous results that required stronger initial data regularity.

## Contribution

It provides a refined decay rate analysis for wave equations with Lipschitz coefficients, relaxing regularity assumptions on initial data compared to prior work.

## Key findings

- Enhanced decay rate estimates for local energy in wave equations with Lipschitz coefficients
- Reduced regularity requirements on initial data for decay analysis
- Comparison with previous log-order decay results

## Abstract

We consider the Cauchy problem for wave equations with variable coefficients in the whole space. We improve the rate of decay of the local energy, which has been recently studied by J. Shapiro, where he derives the log-order decay rates of the local energy under stronger assumptions on the regularity of the initial data.