Asymptotic behavior and dynamic stability of phase mixtures for the equations of Navier–Stokes with nonmonotonic pressure

We investigate the asymptotic behavior of the solutions of the compressible Navier–Stokes equations with nonmonotonic pressure when the initial data is large and discontinuous. We provide sufficient conditions on the pressure function for different boundary-value problems that guarantee strong convergence of the volume variable as time approaches infinity and show that, typically, fairly arbitrary discontinuous static phase mixtures can be realized as time-asymptotic limits from smooth initial data. It is required in the analysis that we improve known existence theories, which typically have small data or time-dependent bounds.