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Relevance of the Slip Condition for Fluid Flows Near an Irregular Boundary

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Abstract

We consider the Navier-Stokes equation in a domain with a rough boundary. The roughness is modeled by a small amplitude and small wavelength oscillation, with typical scale \({\varepsilon \ll 1}\). For periodic oscillation, it is well-known that the best homogenized (that is regular in \({\varepsilon}\)) boundary condition is of Navier type. Such result still holds for random stationary irregularities, as shown recently by the first author [5, 15]. We study here arbitrary irregularity patterns.

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Authors and Affiliations

  1. DMA/CNRS, Ecole Normale Supérieure, 45 rue d’Ulm, 75005, Paris, France

    David Gérard-Varet

  2. Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY, 10012, USA

    Nader Masmoudi

Authors
  1. David Gérard-Varet
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  2. Nader Masmoudi
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Correspondence to David Gérard-Varet.

Additional information

Communicated by P. Constantin

Partially supported by NSF Grant DMS-0703145.

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Gérard-Varet, D., Masmoudi, N. Relevance of the Slip Condition for Fluid Flows Near an Irregular Boundary. Commun. Math. Phys. 295, 99–137 (2010). https://doi.org/10.1007/s00220-009-0976-0

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  • DOI: https://doi.org/10.1007/s00220-009-0976-0

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