  In this paper, we investigate the vanishing viscosity limit for solutions to
the Navier-Stokes equations with a Navier slip boundary condition on general
compact and smooth domains in $\mathbf{R}^3$. We first obtain the higher order
regularity estimates for the solutions to Prandtl's equation boundary layers.
Furthermore, we prove that the strong solution to Navier-Stokes equations
converges to the Eulerian one in $C([0,T];H^1(\Omega))$ and
$L^\infty((0,T)\times\o)$, where $T$ is independent of the viscosity, provided
that initial velocity is regular enough. Furthermore, rates of convergence are
obtained also.
