For inviscid systems, they reduce to the Euler equations.  
Their most general form is derived from the Cauchy momentum equation, usually by first splitting the stress tensor into the deviatoric tensor and the pressure.  By defining separate regimes above and below a critical shear stress, they may be extended to Bingham plastics, while modeling shear stress in terms of a power law allows them to model (*) rheopectic and thixotropic behaviors.  For inviscid systems, they reduce to the Euler equations.  If Newtonian behavior is assumed, they can be derived from the Reynolds transport theorem.  It is an open question whether smooth solutions for them in three dimensions always exist.  For 10 points, name this set of partial differential equations which describe fluid flow.
Their most general form is derived from the Cauchy momentum equation, usually by first splitting the stress tensor into the deviatoric tensor and the pressure.  
{Navier-Stokes} equations (2) [AU]