Rigorous non-dimensionalization of this equation results in the Reynolds number, while integrating it along a streamline collapses it to Bernoulli's equation.  
Neglecting inertial cross-product terms and time-averaging this relation yields a form of the Moore-Greitzer equation.  In standard form, the right hand side of this equation is the local inertia, equal to the density times the Stokes total time derivative of Eulerian velocity.  The solutions of this vector equation probably reside in an infinite-dimensional state space, which would explain its behavior at high parameter values, and most of its complexity arises because it contains the divergence of the viscous stress tensor, ? ["tau"].  Rigorous non-dimensionalization of this equation results in the Reynolds number, while integrating it along a streamline collapses it to Bernoulli's equation.  FTP, identify this partial differential equation that is the form of the momentum balance in a continuum fluid and is named for French and Irish physicists.
Neglecting inertial cross-product terms and time-averaging this relation yields a form of the Moore-Greitzer equation.  
Navier-Stokes equation (do not accept "Euler's equation," which by definition contains no inertial cross-product terms)