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.