Vorticity layers of the 2D Navier-Stokes equations with a slip type boundary condition

We study the asymptotic behavior, at small viscosity ε, of the NavierStokes equations in a 2D curved domain. The Navier-Stokes equations are supplemented with the slip boundary condition, which is a special case of the Navier friction boundary condition where the friction coefficient is equal to two times the curvature on the boundary. We construct an artificial function, which is called a corrector, to balance the discrepancy on the boundary of the Navier-Stokes and Euler vorticities. Then, performing the error analysis on the corrected difference of the Navier Stokes and Euler vorticity equations, we prove convergence results in the L norm in space uniformly in time, and in the norm of H in space and L in time with rates of order ε, and ε respectively. In addition, using the smallness of the corrector, we obtain the convergence of the Navier-Stokes solution to the Euler solution in the H norm uniformly in time with rate of order ε.