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Boundary Asymptotic Analysis for an Incompressible Viscous Flow: Navier Wall Laws

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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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Authors and Affiliations

  1. Département de Mathématiques, FST Tanger, Université Abdelmalek Essaâdi, B.P. 416, Tanger, Morocco

    M. El Jarroudi

  2. Laboratoire de Gestion des Risques et Environnement, Université de Haute-Alsace, 25 rue de Chemnitz, 68200, Mulhouse, France

    A. Brillard

Authors
  1. M. El Jarroudi
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  2. A. Brillard
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Correspondence to A. Brillard.

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El Jarroudi, M., Brillard, A. Boundary Asymptotic Analysis for an Incompressible Viscous Flow: Navier Wall Laws. Appl Math Optim 57, 371–400 (2008). https://doi.org/10.1007/s00245-007-9026-5

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  • DOI: https://doi.org/10.1007/s00245-007-9026-5

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