About new models of slip/no-slip boundary condition in thin film flows

The behaviour of a thin fluid film with a new slip/no slip model (The double parameter slip DPS) on a part of the boundary is studied. From the Stokes equations, the convergence of the velocity, pressure and wall-stress is established. The limit problem is described in terms of a new Reynolds equation involving shear stress and associated with a variational equation. Existence and uniqueness are proved. Relation with the previously known thin film problem with Tresca boundary condition is highlighted. A numerical algorithm is proposed and numerical examples are given.