TY - JOUR

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

AU - Gérard-Varet, David

AU - Masmoudi, Nader

N1 - Funding Information:
Partially supported by NSF Grant DMS-0703145.

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.

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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 -