The solvability of the nonstationary problem for the model system of the barotropic gas flows

Considered an approximate system Navier-Stokes equtions for the compressible viscous barotropic flows. The nonpotential flows are considered. The global existence of the weak solutions for the 3-dimensional problem is obtained. In the case the 2-dimensional the theorem of the existense and uniqueness is proved. The proof of main result is based on a new priori estimates.