  The objective of this work is to present the existence result for the evolu-
tionary compressible Navier-Stokes equations via time discretization. We
consider the two-dimensional case with slip boundary conditions. First, the
existence of weak solution for a fixed time step \Delta t > 0 is presented and
then the limit passage as \Delta t \to 0+ is carried out. The proof is based on
a new technique established for the stedy Navier-Stokes equations by Mucha P.
and Pokorn\'y M. 2006 Nonlinearity 19 1747-1768.
