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

2025/12/16 by Anguiano, María, Suárez-Grau, Francisco J.
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2512.14303

Abstract

This theoretical study deals with the Navier-Stokes equations posed in a 3D thin domain with thickness 0<ε≪ 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 ε^{γ\over s}, with γ∈ ℝ and flow index 1γ_s^* corresponds to a limit boundary condition of type perfect slip. The subcritical case γ<γ_s^* corresponds to a limit boundary condition of type no-slip.

Citations

• Stokes and Navier-Stokes equations with Navier boundary conditions
• Stokes and Navier-Stokes equations with Navier boundary condition
• Nonlinear Reynolds equations for non-Newtonian thin-film fluid flows\n over a rough boundary
• Effective boundary condition at a rough surface starting from a slip condition

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• Navier-Stokes equations in a curved thin domain, Part I: uniform estimates for the Stokes operator
• Approximation of a solution to the stationary Navier-Stokes equations in a curved thin domain by a solution to thin-film limit equations
• The 3-D Inviscid Limit Result under Slip Boundary Conditions. A Negative Answer
• The inviscid limit of Navier-Stokes with critical Navier-slip boundary\n conditions for analytic data