  There are several questions with NS, which include: 1. Both symmetric shear
terms and stretching terms in strain and stress are coordinate-dependent and
thus not Galilean invariant; 2. The physical meaning of both diagonal and
off-diagonal elements are not clear, which is coordinate-dependent; 3. It is
hard to measure the strain and stress quantitatively, and viscosity is really
measured by vorticity not by symmetric strain; 4. There is no vorticity tensor
in NS, which plays important role in fluid flow especially for turbulent flow.
The new proposed governing equations for fluid dynamics use vorticity tensor
only, which is anti-symmetric. The advantages include: 1. Both shear and stress
are anti-symmetric, which are Galilean invariant and independent of coordinate
rotation; 2. The physical meaning of off diagonal elements is clear, which is
anti-symmetric shear stress, 3. Viscosity coefficients are obtained by
experiment which uses vorticity, 4. The vorticity term can be further
decomposed to rigid rotation and anti-symmetric shear, which are important to
turbulence research, 5. The computation cost for viscous term is reduced to
half as the diagonal terms are all zero as six elements are reduced to three.
Several computational results are made, which clearly demonstrate both NS and
new governing equations have exactly same results. As shown below, the new
governing equation is identical to NS in mathematics, but the former has lower
cost and several advantages mentioned above including possibility to better
study turbulent flow. There are reasons to use the new governing equations to
replace Navier-Stokes equations. The unique definition and operation of vector
and tensor by matrix and matrix operation are also discussed in this paper.
