Article Dans Une Revue Applied Mathematics and Optimization Année : 2008

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

Résumé

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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hal-00539904 , version 1 (25-11-2010)

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Mustapha El Jarroudi, Alain Brillard. Boundary Asymptotic Analysis for an Incompressible Viscous Flow: Navier Wall Laws. Applied Mathematics and Optimization, 2008, 57 (3), pp.371-400. ⟨10.1007/s00245-007-9026-5⟩. ⟨hal-00539904⟩
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