Journal
INTERFACES AND FREE BOUNDARIES
Volume 19, Issue 2, Pages 243-271Publisher
EUROPEAN MATHEMATICAL SOC
DOI: 10.4171/IFB/382
Keywords
Fourth order degenerate parabolic equations; thin film equations; free boundary problems; lubrication theory; moving contact line; droplets
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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.
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