Methods and Applications of Analysis

Volume 18 (2011)

Number 2

Weak solutions to lubrication equations in the presence of strong slippage

Pages: 183 – 202

DOI: http://dx.doi.org/10.4310/MAA.2011.v18.n2.a4

Authors

Georgy Kitavtsev (Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany)

Philippe Laurençot (Institut de Mathématiques de Toulouse, Université de Toulouse, France)

Barbara Niethammer (Mathematical Institute, University of Oxford, United Kingdom)

Abstract

The existence of global weak solutions is proved for one-dimensional lubrication models that describe the dewetting process of nanoscopic thin polymer films on hydrophobyzed substrates and take account of large slippage at the polymer-substrate interface. The convergence of these solutions as either the Reynolds number or the capillarity goes to zero, as well as their limiting behaviour as the slip length goes to zero or infinity are investigated.

Keywords

existence, thin film, lubrication equation, slippage

2010 Mathematics Subject Classification

35D30, 35M33, 35Q35, 76D08

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