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arXiv · 2512.14303

Asymptotic analysis of the Navier-Stokes equations in a thin domain with power law slip boundary conditions

María Anguiano·Francisco J. Suárez-Grau
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Abstract

This theoretical study deals with the Navier-Stokes equations posed in a 3D thin domain with thickness $0<\varepsilon\ll 1$, assuming power law slip boundary conditions, with an anisotropic tensor, on the bottom. This condition, introduced in (Djoko et al., Comput. Math. Appl., 128 (2022) 198-213), represents a generalization of the Navier slip boundary condition. The goal is to study the influence of the power law slip boundary conditions with an anisotropic tensor of order $\varepsilon^{\gamma\over s}$, with $\gamma\in \mathbb{R}$ and flow index $1 \gamma_s^*$ corresponds to a limit boundary condition of type perfect slip. The subcritical case $\gamma<\gamma_s^*$ corresponds to a limit boundary condition of type no-slip.

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María Anguiano, Francisco J. Suárez-Grau. 2025-12-16. Asymptotic analysis of the Navier-Stokes equations in a thin domain with power law slip boundary conditions. https://doi.org/10.1002/mana.70011

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