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In this paper, we investigate the vanishing viscosity limit problem for the3-dimensional (3D) incompressible Navier-Stokes equations in a general boundedsmooth 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 thecorresponding solutions of the idea Euler equations with the standard slipboundary condition are obtained.

On the Inviscid Limit of the 3D Navier-Stokes Equations with Generalized Navier-slip Boundary Conditions