Abstract
In this paper, we consider the Brinkman equation in the three-dimensional thin domain Q(e) subset of R-3. The purpose of this paper is to evaluate the asymptotic convergence of a fluid flow in a stationary regime. Firstly, we expose the variational formulation of the posed problem. Then, we presented the problem in transpose form and prove different inequalities for the solution (u(epsilon), p(epsilon)) independently of the parameter epsilon. Finally, these estimates allow us to have the limit problem and the Reynolds equation and establish the uniqueness of the solution.