  We derive the general analytical solution of the viscous hydrodynamic
equations for an ultrarelativistic gas of hard spheres undergoing Bjorken
expansion, taking into account effects from particle number conservation, and
use it to analytically determine its attractor at late times. Differently than
all the cases considered before involving rapidly expanding fluids, in this
example the gradient expansion converges. We exactly determine the hydrodynamic
attractor of this system when its microscopic dynamics is modeled by the
Boltzmann equation with a fully nonlinear collision kernel. The exact late time
attractor of this system can be reasonably described by hydrodynamics even when
the gradients are large.
