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Influence of wall roughness on the slip behaviour of viscous fluids

Published online by Cambridge University Press:  08 October 2008

Dorin Bucur ,
Eduard Feireisl  and
Šárka Nečasová
Dorin Bucur
Affiliation:
Laboratoire de Mathématiques, CNRS UMR 5127, Université de Savoie, Campus Scientifique, 73376 Le-Bourget-Du-Lac, France
Eduard Feireisl
Affiliation:
Mathematical Institute of the Academy of Sciences of the Czech Republic, Žitná 25, 11567 Praha 1, Czech Republic (feireisl@math.cas.cz)
Šárka Nečasová
Affiliation:
Mathematical Institute of the Academy of Sciences of the Czech Republic, Žitná 25, 11567 Praha 1, Czech Republic
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We consider the stationary equations of a general viscous fluid in an infinite (periodic) slab supplemented with Navier's boundary condition with a friction term on the upper part of the boundary. In addition, we assume that the upper part of the boundary is described by a graph of a function φε, where φε oscillates in a specific direction with amplitude proportional to ε. We identify the limit problem when ε → 0, in particular, the effective boundary conditions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 138 , Issue 5 , October 2008 , pp. 957 - 973
Copyright
Copyright © Royal Society of Edinburgh 2008