  This paper concerns the instability and stability of the trivial steady
states of the incompressible Navier-Stokes equations with Navier-slip boundary
conditions in a slab domain in dimension two. The main results show that the
stability (or instability) of this constant equilibrium depends crucially on
whether the boundaries dissipate energy and the strengthen of the viscosity and
slip length. It is shown that in the case that when all the boundaries are
dissipative, then nonlinear asymptotic stability holds true, otherwise, there
is a sharp critical viscosity, which distinguishes the nonlinear stability from
instability.
