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
SN - 0010-3616
VL - 295
SP - 99
EP - 137
JO - Communications In Mathematical Physics
JF - Communications In Mathematical Physics
IS - 1
ER -