On the Fourier Truncation Method for the Rough Data Cubic Defocusing NLW on $\mathbb{H}^3$

Abstract

In this paper, we study the cubic defocusing nonlinear wave equation on the three dimensional hyperbolic space. We use the Fourier truncation method to show that the equation is globally well-posed and scatters if the initial data lies in $H^s(\mathbb{H}^3)$, $s>\frac{182}{201}\approx 0.905$.