  The Navier-Stokes equation contains two terms which have been subjected to
slight modification: (a) the viscosity term depends of time (the viscosity in
average on time is zero, but its variance is non-zero), (b) the pressure
gradient contains an added term describing the quantum entropy gradient
multiplied by the pressure. Owing to these modifications, the Navier-Stokes
equation can be reduced to the Schr\"odinger equation describing behavior of a
particle into the vacuum being as a superfluid medium. Vortex structures
arising in this medium show infinitely long life owing to zeroth average
viscosity. The non-zero variance describes exchange of the vortex energy with
zero-point energy of the vacuum. Radius of the vortex trembles around some
average value. This observation sheds the light to the Zitterbewegung
phenomenon. The long-lived vortex has a non-zero core where the vortex velocity
vanishes.

Quantum Physics;Fluid Dynamics