  We employ Navier-Stokes granular hydrodynamics to investigate the long-time
behavior of clustering instability in a freely cooling dilute granular gas in
two dimensions. We find that, in circular containers, the homogeneous cooling
state (HCS) of the gas loses its stability via a sub-critical pitchfork
bifurcation. There are no time-independent solutions for the gas density in the
supercritical region, and we present analytical and numerical evidence that the
gas develops thermal collapse unarrested by heat diffusion. To get more
insight, we switch to a simpler geometry of a narrow-sector-shaped container.
Here the HCS loses its stability via a transcritical bifurcation. For some
initial conditions a time-independent inhomogeneous density profile sets in,
qualitatively similar to that previously found in a narrow-channel geometry.
For other initial conditions, however, the dilute gas develops thermal collapse
unarrested by heat diffusion. We determine the dynamic scalings of the flow
close to collapse analytically and verify them in hydrodynamic simulations. The
results of this work imply that, in dimension higher than one, Navier-Stokes
hydrodynamics of a dilute granular gas is prone to finite-time density blowups.
This provides a natural explanation to the formation of densely packed clusters
of particles in a variety of initially dilute granular flows.
