Asymptotic Behavior of Viscous Fluids on Rough Boundaries

A relevant problem in fluid mechanics is the appropriate choice of the boundary conditions. For a viscous fluid in a 3D domain, a well accepted hypothesis is that if the boundary is impermeable, then the fluid adheres completely to it. This condition is called adherence condition. However, some other boundary conditions are often used which may be more realistic from a physical point of view. In this sense, for a viscous fluid governed by the Stokes or Navier-Stokes system, Navier proposed a slip-friction boundary condition. In this work we study the relation between both the adherence and the Navier conditions imposed on different types of rough boundaries: periodic and non-periodic.