The role of free work identity in viscous compressible flows

Some consequences of energy identity are discussed, on assumption that there exists a neighborhood of Sb of radius η where the total energy is a minimum. For fluid phase transition the neighborhood where the rest state Sb results in isolated minimum for internal energy has finite radius r that will restrict to zero as basic density b approaches a critical value *. Nonlinear asymptotic stability for barotropic viscous fluids is proved by use of free work identity which enables us to provide a stronger generalized energy inequality. The stability theorem is proved in a class of regular unsteady flows which are supposed to exist. Nonlinear instability for fluid phase change with zero external forces is proved. The goal is reached assuming by absurdum that is stable in L∞ norm.