caa a22 4500 605516057 CHVBK 20210128100712.0 cr unu---uuuuu 210128e20151101xx s 000 0 eng 10.1007/s00205-015-0868-8 doi (NATIONALLICENCE)springer-10.1007/s00205-015-0868-8 Darcy's Flow with Prescribed Contact Angle: Well-Posedness and Lubrication Approximation [Elektronische Daten] [Hans Knüpfer, Nader Masmoudi] 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 . Springer-Verlag Berlin Heidelberg, 2015 Knüpfer Hans University of Heidelberg, Im Neuenheimer Feld 294, 69120, Heidelberg, Germany aut Masmoudi Nader Courant Institute of Mathematical Sciences, 251 Mercer Street, 10012, New York, NY, USA aut Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 218/2(2015-11-01), 589-646 0003-9527 218:2<589 2015 218 205 https://doi.org/10.1007/s00205-015-0868-8 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00205-015-0868-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Knüpfer Hans University of Heidelberg, Im Neuenheimer Feld 294, 69120, Heidelberg, Germany aut NATIONALLICENCE 700 1- Masmoudi Nader Courant Institute of Mathematical Sciences, 251 Mercer Street, 10012, New York, NY, USA aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 218/2(2015-11-01), 589-646 0003-9527 218:2<589 2015 218 205