  Although the existence of dissipative weak solutions for the compressible
Navier-Stokes system has already been established for any finite energy initial
data, uniqueness is still an open problem. The idea is then to select a
solution satisfying the semigroup property, an important feature of systems
with uniqueness. More precisely, we are going to prove the existence of a
semiflow selection in terms of the three state variables: the density, the
momentum and the energy. Finally, we will show that it is possible to introduce
a new selection defined only in terms of the initial density and momentum;
however, the price to pay is that the semigroup property will hold almost
everywhere in time.
