- journal article metadata
European Mathematical Society Publishing House
2017-06-18 23:45:01
Interfaces and Free Boundaries
Interfaces Free Bound.
IFB
1463-9963
1463-9971
Partial differential equations
Numerical analysis
Fluid mechanics
Biology and other natural sciences
10.4171/IFB
http://www.ems-ph.org/doi/10.4171/IFB
subscribers, moving wall 5 years
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
19
2017
2
Weak solutions to thin-film equations with contact-line friction
Maria
Chiricotto
Universität Heidelberg, Germany
Lorenzo
Giacomelli
Università di Roma La Sapienza, Italy
Fourth order degenerate parabolic equations, thin film equations, free boundary problems, lubrication theory, moving contact line, droplets
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.
Partial differential equations
Fluid mechanics
243
271
10.4171/IFB/382
http://www.ems-ph.org/doi/10.4171/IFB/382