Modelling the dynamic contact angle

We consider a fluid system with a free boundary and with a point of contact of the free boundary with a solid wall. We use the instationary Navier-Stokes equations and include surface tension. The correct choice of equations for the angle of contact is an open problem. We present an argument that favors the condition of a constant angle. Since solutions are necessarily of low order of regularity, we have to show the well-posedness of the equations.