Well–posedness for the Navier slip thin–film equation in the case of partial wetting

Consider a viscous liquid droplet spreading on a surface. The classical slip condition at the liquid–solid interface is the no–slip condition. However, this condition lead to infinite dissipation of energy for propagating contact lines (“no–slip paradox”). For this reason other slip conditions such as the Navier–slip have been introduced. We prove well–posedness for a reduced 1–d fluid model modeling Navier slip in the presence of a contact point between air, liquid and solid. The solution space allows for certain types of logarithmic expansions at the moving contact point.