  The vorticity equation stemming from the modified Navier-Stokes equation
gives a solution for a flat profile of the orbital speed of spiral galaxies.
Solutions disclose existence of the Gaussian vortex clouds, the coherent
vortices with infinite life-time, what can be a manifestation of the dark
matter. The solutions also disclose what we might call a breathing of the
galaxies - due to an exchange of the vortex energy with zero-point fluctuations
in the vacuum. .
