  We consider cosmology of the recently introduced mimetic matter with higher
derivatives (HD). Without HD this system describes irrotational dust - Dark
Matter (DM) as we see it on cosmologically large scales. DM particles
correspond to the shift-charges - Noether charges of the shifts in the field
space. Higher derivative corrections usually describe a deviation from the
thermodynamical equilibrium in the relativistic hydrodynamics. Thus we show
that mimetic matter with HD corresponds to an imperfect DM which: i)
renormalises the Newton's constant in the Friedmann equations, ii) has zero
pressure when there is no extra matter in the universe, iii) survives the
inflationary expansion which puts the system on a dynamical attractor with a
vanishing shift-charge, iv) perfectly tracks any external matter on this
attractor, v) can become the main (and possibly the only) source of DM,
provided the shift-symmetry in the HD terms is broken during some small time
interval in the radiation domination era. In the second part of the paper we
present a hydrodynamical description of general anisotropic and inhomogeneous
configurations of the system. This imperfect mimetic fluid has an energy flow
in the field's rest frame. We find that in the Eckart and in the
Landau-Lifshitz frames the mimetic fluid possesses nonvanishing vorticity
appearing already at the first order in the HD. Thus, the structure formation
and gravitational collapse should proceed in a rather different fashion from
the simple irrotational DM models.
