  This paper concerns the Cauchy problem of the barotropic compressible
Navier-Stokes equations on the whole two-dimensional space with vacuum as far
field density. In particular, the initial density can have compact support.
When the shear and the bulk viscosities are a positive constant and a power
function of the density respectively, it is proved that the two-dimensional
Cauchy problem of the compressible Navier-Stokes equations admits a unique
local strong solution provided the initial density decays not too slow at
infinity. Moreover, if the initial data satisfy some additional regularity and
compatibility conditions, the strong solution becomes a classical one.
