Boundary Asymptotic Analysis for an Incompressible Viscous Flow: Navier Wall Laws |
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Authors: | M. El Jarroudi A. Brillard |
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Affiliation: | (1) Département de Mathématiques, FST Tanger, Université Abdelmalek Essaadi, B.P. 416, Tanger, Morocco;(2) Laboratoire de Gestion des Risques et Environnement, Université de Haute-Alsace, 25 rue de Chemnitz, 68200 Mulhouse, France |
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Abstract: | We consider a new way of establishing Navier wall laws. Considering a bounded domain Ω of R N , N=2,3, surrounded by a thin layer Σ ε , along a part Γ2 of its boundary ∂Ω, we consider a Navier-Stokes flow in Ω∪∂Ω∪Σ ε with Reynolds’ number of order 1/ε in Σ ε . Using Γ-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 Γ2. 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. |
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Keywords: | Navier law Navier-Stokes flow Γ -convergence Asymptotic behaviour Optimal control problem |
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