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- W4386875464 abstract "In this paper, we consider the higher-order convergence rates for the 2D stationary and non-stationary Navier-Stokes Equations over highly oscillating periodic bumpy John domains with $C^{2}$ regularity in some neighborhood of the boundary point (0,0). For the stationary case and any $gammain (0,1/2)$, using the variational equation satisfied by the solution and the correctors for the bumpy John domains obtained by Higaki, Prange and Zhuge cite{higaki2021large,MR4619004} after correcting the values on the inflow/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 so called Navier's wall laws, which generalized the results obtained by J{a}ger and Mikeli'{c} cite{MR1813101}. Moreover, for the non-stationary case, using the energy method, we can obtain an $O(varepsilon^{2-gamma}+exp(-Ct))$ convergence rate for the velocity in $L_x^1$." @default.
- W4386875464 created "2023-09-20" @default.
- W4386875464 creator A5085215477 @default.
- W4386875464 date "2023-09-17" @default.
- W4386875464 modified "2023-09-27" @default.
- W4386875464 title "Convergence Rates for the Stationary and Non-stationary Navier-Stokes Equations over Non-Lipschitz Boundaries" @default.
- W4386875464 doi "https://doi.org/10.48550/arxiv.2309.09252" @default.
- W4386875464 hasPublicationYear "2023" @default.
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