Analysis for flow of an incompressible Brinkman-type fluid in thin medium with friction (Q2236417)

Summary: In this paper, we consider the Brinkman equation in the three-dimensional thin domain \(\mathbb{Q}^\varepsilon\subset\mathbb{R}^3\). 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 \(( u^\varepsilon , p^\varepsilon)\) independently of the parameter \(\varepsilon\). Finally, these estimates allow us to have the limit problem and the Reynolds equation and establish the uniqueness of the solution.