Calculus of Variations and Geometric Measure Theory

M. Chiricotto - L. Giacomelli

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

created by giacomelli on 11 Oct 2015
modified on 04 Feb 2021


Published Paper

Inserted: 11 oct 2015
Last Updated: 4 feb 2021

Journal: Interfaces and free boundaries
Year: 2015


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.