A global existence result for a semilinear wave equation with lower order terms on compact Lie groups

TL;DR

This paper proves the global existence of small solutions to a semilinear wave equation with damping, mass, and power nonlinearity on compact Lie groups, using Fourier analysis techniques.

Contribution

It establishes the first global existence result for such equations on compact Lie groups without lower bounds on the nonlinearity exponent p.

Findings

Global solutions exist for small initial data

No lower bounds on p are required for existence

Fourier analysis on Lie groups is effectively used

Abstract

In this paper, we study the semilinear wave equation with lower order terms (damping and mass) and with power type nonlinearity $|u|^p$ on compact Lie groups. We will prove the global in time existence of small data solutions in the evolution energy space without requiring any lower bounds for $p>1$. In our approach, we employ some results from Fourier analysis on compact Lie groups.