Vanishing vertical viscosity limit of anisotropic Navier-Stokes equation with no-slip boundary condition

In this paper, we consider the zero viscosity limit of the anisotropic incompressible Navier-Stokes equations with no-slip boundary condition (see (1.1)) in R+2. We prove that there exist T independently on ε such that the strong solutions of (1.1) convergence to the solution of (1.2) away from the boundary and to solution of (1.3) near the boundary in L∞((0,T),L2∩L∞(R+2)) when the vertical viscosity vanish, provided that the initial velocity is regular enough and we obtain the optimal convergence rate.