  This paper analyzes the Lamb vector divergence, also called the hydrodynamic
charge density, and its implications to the Navier-Stokes system. It is shown
that the pressure field can be always chosen in a way that ensures regularity
of the Navier-Stokes system. The abstract pressure field that ensures
regularity is defined through two partial differential equations, being of the
elliptic kind. The pressure field defined such a way can be interpreted as a
control potential field that keeps the system regular. The controlling pressure
field depends only on the velocity field of the fluid and its derivatives, so
that the result is applicable in any general setting where the initial data is
divergence free, smooth and square-integrable.
