We rigorously carry out a lubrication approximation for a liquid thin film which spreads on a solid, driven by surface tension. We consider a two--dimensional Darcy liquid as simple model case. Of particular interest to us is the codimension--two free boundary, i.\ e.\ the triple junctions where solid, liquid and vapor meet. In the considered regime of complete wetting, the contact angle vanishes throughout the evolution. We show in particular that this contact angle condition is preserved in the lubrication approximation.
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Lorenzo Giacomelli, Felix Otto, Rigorous lubrication approximation. Interfaces Free Bound. 5 (2003), no. 4, pp. 483–529DOI 10.4171/IFB/88