  We study a nonlinear parabolic system for a time dependent solenoidal vector
field on $\Bbb R^3$. The nonlinear term of this new model equations is obtained
slightly modifying that of the Navier-Stokes equations. The system has the same
scaling property and the Galileian invariance as the Navier-Stokes equations.
For such system we prove the global regularity for a smooth initial data.
