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In this paper, we consider the higher-order convergence rates for the 2Dstationary and non-stationary Navier-Stokes Equations over highly oscillatingperiodic bumpy John domains with $C^{2}$ regularity in some neighborhood of theboundary point (0,0). For the stationary case and any $\gamma\in (0,1/2)$,using the variational equation satisfied by the solution and the correctors forthe bumpy John domains obtained by Higaki, Prange and Zhuge\cite{higaki2021large,MR4619004} after correcting the values on theinflow/outflow boundaries $(\{0\}\cup\{1\})\times(0,1)$, we can obtain an$O(\varepsilon^{2-\gamma})$ approximation in $L^2$ for the velocity and an$O(\varepsilon^{2-\gamma})$ convergence rates in $L^1$ approximated by the socalled Navier's wall laws, which generalized the results obtained by J\"{a}gerand Mikeli\'{c} \cite{MR1813101}. Moreover, for the non-stationary case, usingthe energy method, we can obtain an $O(\varepsilon^{2-\gamma}+\exp(-Ct))$convergence rate for the velocity in $L_x^1$.

Convergence Rates for the Stationary and Non-stationary Navier-Stokes Equations over Non-Lipschitz Boundaries