Geodesic
Weak solutions to thin-film equations with contact-line friction
Maria Chiricotto1 ; Lorenzo Giacomelli2
1Universität Heidelberg, Germany
2Università di Roma La Sapienza, Italy
Interfaces and free boundaries, Tome 19 (2017) no. 2, pp. 243-271

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DOI

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.
DOI : 10.4171/ifb/382
Classification : 35-XX, 76-XX
Mots-clés : Fourth order degenerate parabolic equations, thin film equations, free boundary problems, lubrication theory, moving contact line, droplets

Maria Chiricotto  1   ; Lorenzo Giacomelli  2

1 Universität Heidelberg, Germany
2 Università di Roma La Sapienza, Italy 
Maria Chiricotto; Lorenzo Giacomelli. Weak solutions to thin-film equations with contact-line friction. Interfaces and free boundaries, Tome 19 (2017) no. 2, pp. 243-271. doi: 10.4171/ifb/382
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