### 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 ≪ 1. For periodic oscillation, it is well-known that the best homogenized (that is regular in) 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.

Original language | English (US) |
---|---|

Pages (from-to) | 99-137 |

Number of pages | 39 |

Journal | Communications in Mathematical Physics |

Volume | 295 |

Issue number | 1 |

DOIs | |

State | Published - Feb 2010 |

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### ASJC Scopus subject areas

- Mathematical Physics
- Statistical and Nonlinear Physics

### Cite this

*Communications in Mathematical Physics*,

*295*(1), 99-137. https://doi.org/10.1007/s00220-009-0976-0

**Relevance of the slip condition for fluid flows near an irregular boundary.** / Gérard-Varet, David; Masmoudi, Nader.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 295, no. 1, pp. 99-137. https://doi.org/10.1007/s00220-009-0976-0

}

TY - JOUR

T1 - Relevance of the slip condition for fluid flows near an irregular boundary

AU - Gérard-Varet, David

AU - Masmoudi, Nader

PY - 2010/2

Y1 - 2010/2

N2 - 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 ≪ 1. For periodic oscillation, it is well-known that the best homogenized (that is regular in) 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.

AB - 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 ≪ 1. For periodic oscillation, it is well-known that the best homogenized (that is regular in) 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.

UR - http://www.scopus.com/inward/record.url?scp=76349102325&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=76349102325&partnerID=8YFLogxK

U2 - 10.1007/s00220-009-0976-0

DO - 10.1007/s00220-009-0976-0

M3 - Article

AN - SCOPUS:76349102325

VL - 295

SP - 99

EP - 137

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -