Blow-up and sharp lifespan estimates for a weakly coupled system of semilinear wave equations on a compact Lie group

TL;DR

This paper studies finite-time blow-up and lifespan estimates for a coupled wave system on a compact Lie group, highlighting the influence of initial data and lower order terms.

Contribution

It provides new insights into how Cauchy data and lower order terms affect the lifespan of solutions for wave equations on compact Lie groups.

Findings

Blow-up occurs in finite time under certain conditions.

Lifespan estimates depend on initial data and lower order terms.

The analysis extends to wave systems on compact Lie groups.

Abstract

In this paper, we investigate the blow-up in finite time and the corresponding lifespan estimates for a weakly coupled system of wave equations on a compact Lie group. In particular, we show how the Cauchy data and the presence of lower order terms affect the lifespan of local in-time solutions.