Boundary Asymptotic Analysis for an Incompressible Viscous Flow: Navier Wall Laws
- FST Tanger, Universite Abdelmalek Essaadi, Departement de Mathematiques (Morocco)
We consider a new way of establishing Navier wall laws. Considering a bounded domain {omega} of R{sup N}, N=2,3, surrounded by a thin layer {sigma}{sub {epsilon}}, along a part {gamma}{sub 2} of its boundary {partial_derivative}{omega}, we consider a Navier-Stokes flow in {omega} union {partial_derivative}{omega} union {sigma}{sub {epsilon}} with Reynolds' number of order 1/{epsilon} in {sigma}{sub {epsilon}}. Using {gamma}-convergence arguments, we describe the asymptotic behaviour of the solution of this problem and get a general Navier law involving a matrix of Borel measures having the same support contained in the interface {gamma}{sub 2}. We then consider two special cases where we characterize this matrix of measures. As a further application, we consider an optimal control problem within this context.
- OSTI ID:
- 21242045
- Journal Information:
- Applied Mathematics and Optimization, Journal Name: Applied Mathematics and Optimization Journal Issue: 3 Vol. 57; ISSN 0095-4616
- Country of Publication:
- United States
- Language:
- English
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