  We consider the evolution of small rotational perturbations, with azimuthal
symmetry, of the brane-world cosmological models. The equations describing the
temporal, radial, and angular dependence of the perturbations are derived by
taking into account the effects of both scalar and tensor parts of the dark
energy term on the brane. The time decay of the initial rotation is
investigated for several types of equation of state of the ultra-high density
cosmological matter. For an expanding Universe, rotation always decays in the
case of the perfect dragging, for which the angular velocity of the matter on
the brane equals the rotation metric tensor. For non-perfect dragging, the
behavior of the rotation is strongly equation of state dependent. For some
classes of dense matter, like the stiff causal or the Chaplygin gas, the
angular velocity of the matter on the brane is an increasing function of time.
For other types of the ultra-dense matter, like the Hagedorn fluid, rotation is
smoothed out by the expansion of the Universe. Therefore the study of dynamics
of rotational perturbations of brane world models, as well as in general
relativity, could provide some insights on the physical properties and equation
of state of the cosmological fluid filling the very early Universe.
