  The study solves the general solution to 2D steady Navier-Stokes equation for
incompressible flow without vorticity diffusion, which is more general than
Stokes flow. In order to obtain the general solution, two potential functions
are introduced to express the velocity: a vector potential describing the
rotational incompressible flow and a scalar potential describing the
irrotational incompressible flow. The results show that the vorticity equation
expressed with potential functions is a biharmonic function, which means that
the potential functions describing the flow field are polynomials of no more
than fourth degree. For a steady unidirectional shear flow, the velocity and
pressure fields can be described with the vector potential expressed by a
polynomial of third degree. For non unidirectional two-dimensional steady shear
flow, there may be four independent parameters in the two potential functions.
