In this paper, we consider the Brinkman equation in the three-dimensional thin domain
ℚ
ε
⊂
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
ε
,
p
ε
independently of the parameter
ε
. Finally, these estimates allow us to have the limit problem and the Reynolds equation and establish the uniqueness of the solution.