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 ϱb approaches a critical value ϱ*. 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 ϱ is stable in L∞ norm.