  A possibility of the hydrodynamic description of ultracold fermions via the
microscopic derivation of the model is described. Differently truncated
hydrodynamic models are derived and compared. All models are based on the
microscopic many-particle Schr\"{o}dinger equation. Minimal coupling model
based on the continuity and Euler equations are considered. The extended
hydrodynamic model including the independent dynamics of the momentum flux (the
pressure evolution) is derived. Influence of the spin polarization is
described. The short-range interaction is considered in the isotropic limit.
The interaction is considered up to the third order by the interaction radius.
Therefore, the single fluid model of spin-1/2 fermions and the two fluid model
of spin-1/2 fermions are under consideration in this paper. Spectra of bulk
collective excitations are derived and compared in terms of different models.
