Darcy's Flow with Prescribed Contact Angle: Well-Posedness and Lubrication Approximation
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| 003 | CHVBK | ||
| 005 | 20210128100712.0 | ||
| 007 | cr unu---uuuuu | ||
| 008 | 210128e20151101xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s00205-015-0868-8 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00205-015-0868-8 | ||
| 245 | 0 | 0 | |a Darcy's Flow with Prescribed Contact Angle: Well-Posedness and Lubrication Approximation |h [Elektronische Daten] |c [Hans Knüpfer, Nader Masmoudi] |
| 520 | 3 | |a We consider the spreading of a thin two-dimensional droplet on a solid substrate. We use a model for viscous fluids where the evolution is governed by Darcy's law. At the contact point where air and liquid meet the solid substrate, a constant, non-zero contact angle (partial wetting) is assumed. We show local and global well-posedness of this free boundary problem in the presence of the moving contact point. Our estimates are uniform in the contact angle assumed by the liquid at the contact point. In the so-called lubrication approximation (long-wave limit) we show that the solutions converge to the solution of a one-dimensional degenerate parabolic fourth order equation which belongs to a family of thin-film equations. The main technical difficulty is to describe the evolution of the non-smooth domain and to identify suitable spaces that capture the transition to the asymptotic model uniformly in the small parameter $${\varepsilon}$$ ε . | |
| 540 | |a Springer-Verlag Berlin Heidelberg, 2015 | ||
| 700 | 1 | |a Knüpfer |D Hans |u University of Heidelberg, Im Neuenheimer Feld 294, 69120, Heidelberg, Germany |4 aut | |
| 700 | 1 | |a Masmoudi |D Nader |u Courant Institute of Mathematical Sciences, 251 Mercer Street, 10012, New York, NY, USA |4 aut | |
| 773 | 0 | |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 218/2(2015-11-01), 589-646 |x 0003-9527 |q 218:2<589 |1 2015 |2 218 |o 205 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00205-015-0868-8 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00205-015-0868-8 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Knüpfer |D Hans |u University of Heidelberg, Im Neuenheimer Feld 294, 69120, Heidelberg, Germany |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Masmoudi |D Nader |u Courant Institute of Mathematical Sciences, 251 Mercer Street, 10012, New York, NY, USA |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 218/2(2015-11-01), 589-646 |x 0003-9527 |q 218:2<589 |1 2015 |2 218 |o 205 | ||