Very interestingly, for a significant fraction of the following evolution, the shaping of the cosmic web under the Zeldovich approximation proceeds without even taking into account the effect of the mutual gravitational interaction of particles - they just fly apart, keeping memory of the initial perturbation, until they get denser in regions where the flows converge.
After this, the approximation is not valid anymore - because particles must "feel each other", somehow (gravity & collisions)