  When one considers a shock wave in the frame where the shock is at rest, on
either side one has a steady flow which converges to equilibrium away from the
shock. However, hydrodynamics is unable to describe this flow if the asymptotic
velocity is higher than the characteristic speed of the theory. We obtain an
exact solution for the decay rate to equilibrium for a conformal fluid in
kinetic theory under the relaxation time approximation, and compare it to two
hydrodynamic schemes, one accounting for the second moments of the distribution
function and thus equivalent, in the small deviations from equilibrium limit,
to an Israel-Stewart framework, and another accounting for both second and
third moments. While still having a finite characteristic speed, the second
model is a significant improvement on the first.
