  We examine the large-time behaviour of solutions to the compressible
Navier-Stokes equations under the assumption of radial symmetry. In particular,
we calculate a fast time-decay estimate of the norm of the nonlinear part of
the solution. This allows us to obtain a bound from below for the time-decay of
the solution in $L^\infty$, proving that our decay estimate in that space is
sharp. The decay rate is the same as that of the linear problem for curl-free
flow. We also obtain an estimate for a scalar system related to curl-free
solutions to the compressible Navier-Stokes equations in a weighted Lebesgue
space.
