Asymptotics of homogeneous oscillations in a compressible viscous fluid

The large amplitude high frequency oscillations of the flow of a compressible viscous fluid have been shown to obey to an integro-differential system. We consider here the case of homogeneous oscillations, with both gas-like pressure law and a van der Waals one. We show that the solution admits a limit as the time increases. This limit is constant in the former case, but may take up to three distinct values in the latter.