Weak solutions to thin-film equations with contact-line friction

  • Maria Chiricotto

    Universität Heidelberg, Germany
  • Lorenzo Giacomelli

    Università di Roma La Sapienza, Italy


We consider the thin-film equation with a prototypical contact-line condition modeling the effect of frictional forces at the contact line where liquid, solid, and air meet. We show that such condition, relating flux with contact angle, naturally emerges from applying a thermodynamic argument due to Weiqing Ren and Weinan E [Commun. Math. Sci. 9 (2011), 597–606] directly into the framework of lubrication approximation. For the resulting free boundary problem, we prove global existence of weak solutions, as well as global existence and uniqueness of approximating solutions which satisfy the contact line condition pointwise. The analysis crucially relies on new contractivity estimates for the location of the free boundary.

Cite this article

Maria Chiricotto, Lorenzo Giacomelli, Weak solutions to thin-film equations with contact-line friction. Interfaces Free Bound. 19 (2017), no. 2, pp. 243–271

DOI 10.4171/IFB/382