# Strichartz estimates for the one-dimensional wave equation

## TL;DR

This paper establishes Strichartz estimates for the one-dimensional wave equation with potential, decomposing solutions into spectral and radiation parts, and applies these results to analyze Yang-Mills fields on wormhole spacetimes.

## Contribution

It provides the first Strichartz estimates for the perturbed 1D wave equation and applies them to long-time behavior of Yang-Mills fields.

## Key findings

- Decomposition of wave evolution into spectral and radiation parts.
- Proof of Strichartz estimates for the radiation component.
- Application to long-time asymptotics of Yang-Mills fields.

## Abstract

We study the hyperboloidal initial value problem for the one-dimensional wave equation perturbed by a smooth potential. We show that the evolution decomposes into a finite-dimensional spectral part and an infinite-dimensional radiation part. For the radiation part we prove a set of Strichartz estimates. As an application we study the long-time asymptotics of Yang-Mills fields on a wormhole spacetime.