Analysis of semidiscretization of the compressible Navier-Stokes equations

The objective of this work is to present the existence result of for the non- steady compressible Navier-Stokes equations via time discretization. We consider the two-dimensional case with a slip boundary conditions. First, the existence of weak solution for a fixed length of time interval \Delta t > 0 is presented and then the limit passage as \Delta t \rightarrow 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.