At present we imagine themselves the physical vacuum as a superfluid quantum fluid containing enormous amount of particle-antiparticle pairs arising and annihilating continuously. It is the Bose-Einstein condensate existing at super low temperatures of the cosmic space. It is proposed at present also that the dark matter is described as collective excitations of a cold atom Bose-Einstein condensates. Then a motion of this cold superfluid quantum medium can be described in the nonrelativistic limit by pair of equations - the Navier-Stokes equation and the continuity equation. However, the first equation describes the motion of a classical viscous fluid. We need to modify this equation. ....