Geodesic
On the Navier-Stokes equations with anisotropic wall slip conditions
Applications of Mathematics, Tome 68 (2023) no. 1, pp. 1-14.

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This article deals with the solvability of the boundary-value problem for the Navier-Stokes equations with a direction-dependent Navier type slip boundary condition in a bounded domain. Such problems arise when steady flows of fluids in domains with rough boundaries are approximated as flows in domains with smooth boundaries. It is proved by means of the Galerkin method that the boundary-value problem has a unique weak solution when the body force and the variability of the surface friction are sufficiently small compared to the viscosity and the surface friction.
DOI : 10.21136/AM.2021.0079-21
Classification : 76D03, 76D05, 76D07
Keywords: Navier-Stokes equations; Stokes equations; rough boundary; slip boundary condition 
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Le Roux, Christiaan. On the Navier-Stokes equations with anisotropic wall slip conditions. Applications of Mathematics, Tome 68 (2023) no. 1, pp. 1-14. doi : 10.21136/AM.2021.0079-21. http://geodesic.mathdoc.fr/articles/10.21136/AM.2021.0079-21/

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