Boundary asymptotic analysis for an incompressible viscous flow: Navier wall laws

We consider a new way of establishing Navier wall laws. Considering a bounded domain Omega of R(N), N=2,3, surrounded by a thin layer Sigma(epsilon) , along a part Gamma(2) of its boundary partial derivative Omega, we consider a Navier-Stokes flow in Omega boolean OR partial derivative Omega boolean OR Sigma(epsilon) with Reynolds' number of order 1/epsilon in Sigma(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(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.