  Large-scale structure formation is studied in a kinetic theory approach,
extending the standard perfect pressureless fluid description for dark matter
by including the velocity dispersion tensor as a dynamical degree of freedom.
The evolution of power spectra for density, velocity and velocity dispersion
degrees of freedom is investigated in a non-perturbative approximation scheme
based on the Dyson$\unicode{x2013}$Schwinger equation. In particular, the
generation of vorticity and velocity dispersion is studied and predictions for
the corresponding power spectra are made, which qualitatively agree well with
results obtained from $N$-body simulations. It is found that velocity
dispersion grows strongly due to non-linear effects and at late times its mean
value seems to be largely independent of the initial conditions. By taking this
into account, a rather realistic picture of non-linear large-scale structure
formation can be obtained, albeit the numerical treatment remains challenging,
especially for very cold dark matter models.
