# Global existence for a coupled wave system related to the Strauss conjecture

## TL;DR

This paper proves global existence for a coupled semilinear wave system related to the Strauss conjecture, extending previous results and demonstrating stability under perturbations of the spacetime.

## Contribution

It establishes small data global existence for coupled wave equations near the Strauss critical power, including stability under asymptotically flat perturbations.

## Key findings

- Global existence for coupled wave systems proved
- Reduced power threshold below Strauss critical power
- Stability under spacetime perturbations demonstrated

## Abstract

A coupled system of semilinear wave equations is considered, and a small data global existence result related to the Strauss conjecture is proved. Previous results have shown that one of the powers may be reduced below the critical power for the Strauss conjecture provided the other power sufficiently exceeds such. The stability of such results under asymptotically flat perturbations of the space-time where an integrated local energy decay estimate is available is established.