Asymptotic behaviour of pressure and stresses in a thin film flow with a rough boundary
Nadia Benhaboucha, Michèle Chambat, Ionel Sorin Ciuperca · Quarterly of Applied Mathematics · 2005
We study the asymptotic behaviour of an incompressible viscous flow in a narrow gap with a thickness of order $\eta$ and a rough surface. The roughness is defined by a quasi-periodical function with period $\epsilon$. In both cases, when $\eta$ is smaller or at the same order as $\epsilon$, we obtain different Reynolds equations for the pressure. We have also studied the convergence of the stresses on the rough boundary and we discuss the different cases.