I believe that the author means that the equation does not describe a dynamical situation. After any change in the system, the density and the stress is assumed to come into equilibrium very fast (compared to the time-scale of the phenomena the author is trying to study). The dynamics of how this equilibrium occurs is neclected.
You could think of a weight suspended on a spring. If mass is added slowly to the weight then it is a good approximation to simply assume that the lenght of the spring is at the changed equilibrium position. Do it quickly however and the lenght will osccilate.