  This paper concerns with the stability of the plane Couette flow resulted
from the motions of boundaries that the top boundary $\Sigma_1$ and the bottom
one $\Sigma_0$ move with constant velocities $(a,0)$ and $(b,0)$, respectively.
If one imposes Dirichlet boundary condition on the top boundary and Navier
boundary condition on the bottom boundary with Navier coefficient $\alpha$,
there always exists a plane Couette flow which is exponentially stable for
nonnegative $\alpha$ and any positive viscosity $\mu$ and any $a, b \in
\mathbb{R}$, or, for $\alpha<0$ but viscosity $\mu$ and the moving velocities
of boundaries $(a,0), (b,0)$ satisfy some conditions stated in Theorem 1.1.
However, if we impose Navier boundary conditions on both boundaries with Navier
coefficients $\alpha_0$ and $\alpha_1$, then it is proved that there also
exists a plane Couette flow (including constant flow or trivial steady states)
which is exponentially stable provided that any one of two conditions on
$\alpha_0,\alpha_1$, $a, b$ and $\mu$ in Theorem 1.2 holds. Therefore, the
known results for the stability of incompressible Couette flow to no-slip
(Dirichlet) boundary value problems are extended to the Navier boundary value
problems.
