Decay of the kinetic and the thermal energy of compressible viscous fluids

The problem of a heat conducting Navier-Stokes compressible fluid at rest in a rigid container is studied. It is not assumed, as is generally the case, that the rate at which body forces do work balances the rate of work done by hydrostatic pressure. It is shown that the thermal and kinetic energy of arbitrary disturbances of the rest state eventually decays.