  In this article, stabilization result for the viscoelastic fluid flow problem
governed by Kelvin-Voigt model, that is, convergence of the unsteady solution
to a steady state solution is proved under the assumption that linearized
self-adjoint steady state eigenvalue problem has a minimal positive eigenvalue.
Both power and exponential convergence results are derived under various
conditions on the forcing function. It is shown that results are valid
uniformly in the time relaxation or some times called regularization parameter
$\kappa$ as $\kappa\to 0$, which in turn, establishes results for the
Navier-Stokes system.
