  We compute the Euclidean correlators of the stress tensor in pure $SU(3)$
Yang-Mills theory at finite temperature at zero and finite spatial momenta with
lattice simulations. We perform continuum extrapolations using
$N_\tau=10,12,16,20$ lattices with renormalized anisotropy 2. We use these
correlators to estimate the shear viscosity of the gluon plasma in the
deconfined phase. For $T=1.5T_c$ we obtain $\eta/s=0.17(2)$.
