2-DIMENSIONAL STOKES FLOWS WITH SLIP-STICK BOUNDARY-CONDITIONS

We derive the necessary condition for the existence of a solution of the biharmonic equation for general boundary conditions. Making use of this result, we derive a necessary condition in terms of the basic flow, for the existence of a solution for Stokes flow past a circular cylinder with slip-stick boundary conditions. We state and prove a circle theorem when the basic flow satisfies the necessary condition.