On construction of quasi-gasdynamic systems of equations and the barotropic system with the potential body force

A short approach is described for constructing barotropic quasi-gasdynamic (QGD) system of equations by means of a special regularization in time of the barotropic Navier–Stokes system of equations. The approach is generalized to the case of the QGD system with general equations of gas state, a body force and a heat source. For the barotropic QGD system with the potential body force, the pointwise energy balance law is derived. The integral energy balance law and global energy bounds are established as corollaries. For the linearized at the equilibrium solution barotropic QGD system with the potential body force, the exponential in time stabilization of solutions to zero is given.