  We consider the compressible three dimensional Navier Stokes and Euler
equations. In a suitable regime of barotropic laws, we construct a set of
finite energy smooth initial data for which the corresponding solutions to both
equations implode (with infinite density) at a later time at a point, and
completely describe the associated formation of singularity. Two essential
steps of the analysis are the existence of $\mathcal C^\infty$ smooth
self-similar solutions to the compressible Euler equations for quantized values
of the speed and the derivation of spectral gap estimates for the associated
linearized flow which are addressed in the companion papers \cite{MRRSprofile,
MRRSdefoc}. All blow up dynamics obtained for the Navier-Stokes problem are of
type II (non self-similar).
