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On the Navier-Stokes equations with anisotropic wall slip conditions

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Abstract

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.

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Acknowledgement

The author thanks the reviewers for their comments which helped to improve the article.

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Correspondence to Christiaan Le Roux.

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Le Roux, C. On the Navier-Stokes equations with anisotropic wall slip conditions. Appl Math 68, 1–14 (2023). https://doi.org/10.21136/AM.2021.0079-21

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  • DOI: https://doi.org/10.21136/AM.2021.0079-21

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