  In this paper, we investigate the vanishing viscosity limit problem for the
3-dimensional (3D) incompressible Navier-Stokes equations in a general bounded
smooth domain of $R^3$ with the generalized Navier-slip boundary conditions
(\ref{VSg}). Some uniform estimates on rates of convergence in
$C([0,T],L^2(\Omega))$ and $C([0,T],H^1(\Omega))$ of the solutions to the
corresponding solutions of the idea Euler equations with the standard slip
boundary condition are obtained.
