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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 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 (Ω)) and L ∞ ((0, T ) × Ω), where T is independent of the viscosity, provided that initial velocity is regular enough. Furthermore, rates of convergence are obtained also.

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