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• W2023482783 abstract "We study the asymptotic behavior of the solutions of the Navier--Stokes system in a thin domain $Omega_varepsilon$ of thickness $varepsilon$ satisfying the Navier boundary condition on a periodic rough set $Gamma_varepsilonsubset partialOmega_varepsilon$ of period $r_varepsilon$ and amplitude $delta_varepsilon$, with $delta_varepsilon ll r_varepsilon ll varepsilon$. We prove that the limit behavior as $varepsilon$ goes to zero depends on the limit $lambda$ of $delta_varepsilon varepsilon^{1over 2}/r_varepsilon^{3over 2}$. Namely, if $lambda=+infty$, the roughness is so strong that the fluid behaves as if we had imposed the adherence condition on $Gamma_varepsilon$. If $lambda=0$, the roughness is too weak and the fluid behaves as if $Gamma_varepsilon$ were a plane. Finally, if $lambdain(0,+infty)$, the roughness is strong enough to make a new friction term appear in the limit." @default.
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• W2023482783 date "2013-01-01" @default.
• W2023482783 modified "2023-10-18" @default.
• W2023482783 title "Asymptotic Behavior of the Navier--Stokes System in a Thin Domain with Navier Condition on a Slightly Rough Boundary" @default.
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• W2023482783 doi "https://doi.org/10.1137/120873479" @default.
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