  In this note, by constructing suitable approximate solutions, we prove the
existence of global weak solutions to the compressible Navier-Stokes equations
with density-dependent viscosity coefficients in the whole space
$\mathbb{R}^N$, $N\geq2$ (or exterior domain), when the initial data are
spherically symmetric. In particular, we prove the existence of spherically
symmetric solutions to the Saint-Venant model for shallow water in the whole
space (or exterior domain).
