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

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 $H^s({\mathbb{H}}^3)$, $s>\frac{182}{201}\approx 0.905$.